a fluidized immunoadsorption device for removing beta-2

1

A Fluidized Immunoadsorption Device for Removing Beta-2-Microglobulin from Whole Blood:

A Potential Treatment for Dialysis-Related Amyloidosis by

Eric A. Grovender

B.S. Chemical Engineering Iowa State University, 1996

SUBMITTED TO THE DEPARTMENT OF CHEMICAL ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY

JUNE 2003

© 2003 Massachusetts Institute of Technology. All rights reserved.

Signature of Author _________________________________________________________

Department of Chemical Engineering April 14, 2003

Certified by _________________________________________________________

Robert Langer Germeshausen Professor of Chemical and Biomedical Engineering

Thesis Supervisor

Accepted by _________________________________________________________

Daniel Blankschtein Professor of Chemical Engineering

Chairman, Department Graduate Committee

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This Doctoral Thesis has been examined by the following Thesis Committee: Robert Langer, Sc.D. Thesis Supervisor Germeshausen Professor of Chemical and Biomedical Engineering Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts Charles Cooney, Ph.D. Professor Department of Chemical Engineering Massachusetts Institute of Technology Hidde Ploegh, Ph.D. Professor Department of Pathology Harvard Medical School Boston, Massachusetts Maria Rupnick, M.D., Ph.D. Division of Cardiovascular Medicine Brigham and Women�s Hospital Boston, Massachusetts

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A Fluidized Immunoadsorption Device for Removing Beta-2-microglobulin from Whole Blood:

A Potential Treatment for Dialysis-Related Amyloidosis

by

Eric A. Grovender

Submitted to the Department of Chemical Engineering on April 14, 2003 in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Chemical Engineering

Abstract

Dialysis-related amyloidosis (DRA) is a frequent complication of end-stage renal

disease that has been associated with the accumulation of β2-microglobulin (β2m).

Excluding transplantation, existing kidney replacement technologies are believed to remove

insufficient quantities of β2m for the prevention of DRA, as they are non-specific and based

on size-exclusion. A proposed DRA therapy is to use immunoadsorptive particles within an

extracorporeal Vortex Flow Plasmapheretic Reactor (VFPR) to specifically remove β2m from

blood. The compartmental design of the VFPR allows for the use of small adsorbent

particles (~100 µm) that possess inherent mass-transfer advantages over the larger ones

(>400 µm) that are required for safe contact with whole blood for this application.

Demonstrating the efficacy of this technology as a therapy for DRA would support its

tailored application for treating other pathologies that are caused by circulating compounds

such as sepsis, liver failure, autoimmune disease, drug overdoses, and genetic disorders.

Whole anti-β2m antibodies (BBM.1) were immobilized onto agarose beads and used

within a VFPR to remove donor baseline and defined quantities of recombinant β2m from

whole human blood, in vitro. A dynamic immunoadsorption model was developed for the

VFPR that was based upon the independent characterization of the mass-transfer processes

within the VFPR and the thermodynamics of the immunoadsorbent. The experimentally-

observed and model-predicted dynamics of β2m clearance from the blood indicate that the

process controlling the rate of β2m removal was the hemofiltration rate (50 mL-plasma/min),

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which was on the order of the reported supply rate of β2m into the vasculature (70 mL-

plasma/min).

Single-chain variable region (scFv) antibody fragments offer several potential

advantages over whole antibodies due to their size and genetic definition, as well as their

amenability for microbial expression and in vitro evolution. Hence, a BBM.1 scFv was

expressed by a yeast display vector and its affinity was quantified with a fluorescence-

activated cell sorter (KD = 0.008 ± 0.004 mg-β2m/L). Soluble scFv was secreted by yeast and

immobilized onto agarose beads (adsorption site density of 0.41 ± 0.01 mg-β2m/mL-settled-

gel). These results support the feasibility of using the proposed therapy to treat and/or

prevent DRA.

Thesis Supervisor: Robert Langer Title: Germeshausen Professor of Chemical and Biomedical Engineering

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Acknowledgements

I would like to thank my thesis advisor, Professor Robert Langer, for providing me

with the opportunity and privilege of working in his laboratory on this project. Throughout

my tenure, the faith that Bob has exhibited in my abilities as a researcher has encouraged and

inspired me as an engineer and scientist. There are many members of the Langer Laboratory

who have been very helpful over the years, but it is not feasible for me to thank them all here

by name. However, I would like to specifically thank Guillermo Ameer, who is now an

Assistant Professor of Biomedical Engineering at Northwestern University, for being my

friend and mentor over the past five or six years. His support and advice have been an

invaluable part of my graduate school experience. I am also grateful for the work that has

been performed on this project by several undergraduate researchers at MIT, specifically:

David Ting, Helen Lee, Amy Kittredge, Angela Won, and Eric Lau.

I am thankful for the support and guidance that I have received from the members of

my Thesis Committee. This research project would have never occurred without Dr. Maria

Rupnick, as she was its original champion. Meanwhile, Professor Charlie Cooney provided

valuable advice regarding the mathematical modeling of the Vortex Flow Plasmapheretic

Reactor. Professor Hidde Ploegh has graciously contributed his expertise in the field of

immunology to the project, while several members of his research group have been very

helpful with the production of recombinant human β2-microglobulin, including: Madelone

Maurice, Ben Gewurz, Evelyn Wang, and Fleur Sernee.

While they did not serve my Thesis Committee, two other MIT professors also have

been extremely helpful. The development of the scFv-based immunoadsorbent may not have

been possible without the collaboration of Professor K. Dane Wittrup (Chemical

Engineering) and several members of his laboratory, including: Brenda Kellogg, Andy

Yeung, Jeffrey Swers, and Katarina Midelfort. The refolding yield of the recombinant

human β2-microglobulin was drastically increased by following the advice of Professor

Jonathan King (Biology) and his post-doc, Stephen Raso.

I had several outstanding professors as an undergraduate at Iowa State University

whom I would like to thank for their teaching, mentorship, and guidance. I would like to

specifically acknowledge Professor Richard Seagrave who was the most dynamic and

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engaging lecturer one could imagine and inspired me to earn my Ph.D. Furthermore, I am

forever grateful to Dr. Carole Heath, now at Immunex, for introducing me to the field of

bioengineering as a sophomore and providing me with the opportunity to conduct my

undergraduate independent research project. There are two teachers at Woodbury Senior

High School (Minnesota) whose courses I believe laid the foundation for the success that I

experienced at ISU and MIT. They are Judy Trepka and Brian Bonfig who taught Advanced

Placement Chemistry and Advanced Placement Calculus, respectively. America desperately

needs more teachers such as them.

I would like to thank my entire family and all of my friends for supporting me

throughout my 24-year education. I am particularly grateful to both of my parents for always

caring about and encouraging my academic success and achievement. I can still remember

experimenting with electric circuits and chemistry sets at a very young age (well under 10

years old) with my Father. I also appreciate all of the support I received and time invested in

me by my Mother throughout my competitive swimming career, which I believe has helped

me more with my academic career than any single course that I have ever taken.

Finally, I would like to thank Kim Bigelow, my girlfriend throughout most of my

graduate education, for all of her love, friendship, support and understanding.

Eric A. Grovender April 2003 This material is based on work supported under a National Science Foundation Graduate Fellowship as well as a National Institutes of Health Biotechnology Training Grant.

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Biographical Sketch (Curriculum Vitae) for

Eric A. Grovender Education Ph.D. Chemical Engineering, Massachusetts Institute of Technology, Spring 2003

GPA: 4.50/5.00 Thesis Advisor: Robert S. Langer Thesis Title: �A Fluidized Immunoadsorption Device for Removing Beta-2-Microglobulin from Whole Blood: A Potential Treatment for Dialysis-Related Amyloidosis� Thesis Description: Developed a biotherapeutic device to remove a specific protein (β2-microglobulin) from blood that forms solid deposits throughout the bodies of kidney dialysis patients • Engineered a single-chain variable region (scFv) antibody fragment via yeast display • Purified immunoglobulin proteins secreted by yeast and hybridoma cells • Scaled-up production (>100 mg) of recombinant human β2-microglobulin expressed in E.

coli • Tested the feasibility of the proposed therapy through in vitro experimentation with

human blood • Characterized the mass-transfer and thermodynamic behavior of the novel biomedical

device • Developed a mathematical device model, based on chemical engineering fundamentals Biology Minor: Courses in immunology, genetics, biochemistry, cell/tissue engineering, and controlled release drug delivery B.S. Chemical Engineering, Iowa State University, Ames, IA, 1996 GPA: 3.99/4.00 Independent Tissue Engineering Research Project: �Estimation of the Specific Oxygen and Glucose Uptake Rates of Chondrocytes Living in Cartilage Grown In Vitro.� Biology Elective Courses: Biochemistry, Bioprocess Engineering Extracurricular: Men�s Intercollegiate Swimming Team (Division I)

Industrial Medtronic MiniMed, Northridge (Los Angeles), CA Position: Senior Scientist, Sensor Research and Development, starting May 19, 2003

Abbott Laboratories, Chemical and Agricultural Products Division, North Chicago, IL Position: Intern with the Tissue Culture Department, summer 1996 • Identified glutamine as the potential limiting nutrient in the culture of Chinese hamster

ovary (CHO) cells • Presented research findings to the department, including management (oral and written) 3M Company, Engineering Systems and Technology Group, St. Paul, MN Positions: Graduate Intern, Jan-July 1997; Contract Employee, summer 1995 • Designed and built the graphical user interface (GUI) for a drying process simulation

program which enabled its distribution to manufacturing facilities • Created a shareware database of coating solution physical parameters for the drying

process simulation program Cargill, Oilseeds Division, Des Moines, IA Position: Process Engineering Intern, summer 1994 • Performed an energy balance on the refining process which discovered that the majority

of the oil feed stream was bypassing a key heat exchanger • Supervised plant operators and contractors

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Leadership Teaching Assistant, MIT Chemical Engineering Senior Design Course, 2001 Assistant Coach, Boy�s Varsity Swimming Team, St. Paul Central H.S. (MN), 1995-1997

Biology Tissue culture, yeast & bacterial fermentation, PCR, inclusion body refolding, yeast display of Lab Skills proteins, size exclusion and affinity chromatography, antibody/protein engineering, FACS,

radioimmunoassay, protein and DNA electrophoresis, Western blots Hobbies Wilderness camping, fishing, canoeing, backpacking, cycling, running,

triathlons, SCUBA diving Computer Visual Basic for Applications, FORTRAN, Lotus Notes, Word, Excel, PowerPoint, Skills Windows/DOS, software & hardware maintenance Awards National Institutes of Health Biotechnology Training Grant, 2000-2003

National Science Foundation Graduate Fellowship, 1997-2000 ISU Engineering College Senior Scholastic Award (one of top 3 graduates), 1997 Iowa State University Chemical Engineering Department Junior and Senior of the Year, 1995 AIChE Donald F. Othmer Sophomore Academic Excellence Award, 1994 NCAA Academic All-Big 8 Conference Swimming Team, 1993 & 1994

Papers �Single-Chain Antibody Fragment-Based Adsorbent for the Extracorporeal Removal of

β2-microglobulin.� In Preparation.

�Immunoadsorption Model for a Novel Fluidized-bed Blood Detoxification Device.� EA Grovender, CL Cooney, R Langer, and GA Ameer. AIChE Journal 48 (2002): 2357-2365. �Modeling the Mixing Behavior of a Novel Fluidized Extracorporeal Immunoadsorber.� EA Grovender, GA Ameer, CL Cooney and RS Langer. Chemical Engineering Science 56 (2001): 5437-5441. �A Novel Immunoadsorption Device for Removing β2-microglobulin from Whole Blood.� GA Ameer & EA Grovender, H Ploegh, D Ting, WF Owen, M Rupnick, and R Langer. Kidney International 59 (2001): 1544-1550. �RTD Analysis of a Novel Taylor-Couette Flow Device for Blood Detoxification.� GA Ameer, EA Grovender, B Obradovic, CL Cooney, and R Langer. AIChE Journal 45 (1999): 633-638.

Patent �Apparatus for Treating Whole Blood Comprising Concentric Cylinders Defining an Annulus There Between.� G Ameer, RS Langer, M Rupnick, HL Ploegh and EA Grovender, US Patent No. 6,099,730 (2000).

Presentations �Mixing Behavior of a Novel Fluidized-bed Blood Detoxification Device.� International

Society for Blood Purification Annual Meeting, Tokyo (2001). �Dynamic Modeling of a Fluidized Bed Immunoadsorber for Therapeutic Blood Detoxification.� American Institute of Chemical Engineers National Meeting, Los Angeles (2000). �Therapeutic Blood Detoxification via an Immunoadsorptive Fluidized Bed.� Biomedical Engineering Society National Meeting, Seattle (2000).

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Table of Contents Title Page ..............................................................................................1 Committee Page ...................................................................................3 Abstract ................................................................................................5 Acknowledgements..............................................................................7 Biographical Sketch (Curriculum Vitae) .............................................9 Table of Contents...............................................................................11 List of Figures ....................................................................................15 List of Tables ......................................................................................17 Chapter 1: Introduction.....................................................................19

1.1 MOTIVATION ........................................................................................................... 19 1.2 SPECIFIC AIMS ........................................................................................................ 23 1.3 THE VORTEX FLOW PLASMAPHERETIC REACTOR (VFPR) .................... 24 1.4 REFERENCES............................................................................................................ 27

Chapter 2: In Vitro Removal of ββββ2-Microglobulin from Human Blood with an Immunoadsorptive VFPR......................................................31

2.1 INTRODUCTION ...................................................................................................... 31 2.2 METHODS.................................................................................................................. 31

2.2.1 Assays .................................................................................................................... 31 2.2.2 Protein Immobilization........................................................................................ 32 2.2.3 Recombinant ββββ2m Preparation ........................................................................... 32 2.2.4 Capacity of the Immunoadsorptive Media ........................................................ 33 2.2.5 Clearance of ββββ2m from Whole Blood by a VFPR in a Closed-Loop Circuit .. 34 2.2.6 Statistical Analysis ............................................................................................... 35

2.3 RESULTS .................................................................................................................... 35 2.3.1 Protein Immobilization........................................................................................ 35 2.3.2 Capacity of the Immunoadsorptive Media ........................................................ 35 2.3.3 Clearance of ββββ2m from Human Blood with an Immunoadsorptive VFPR..... 36

2.4 DISCUSSION.............................................................................................................. 38 2.5 REFERENCES............................................................................................................ 42

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Chapter 3: Macroscopic Mixing Model for the VFPR...................... 45 3.1 INTRODUCTION ...................................................................................................... 45 3.2 METHODS.................................................................................................................. 45

3.2.1 Reactor Prototypes............................................................................................... 45 3.2.2 Residence Time Distribution Experiments........................................................ 46 3.2.3 Mathematical Modeling....................................................................................... 47

3.3 RESULTS AND DISCUSSION ................................................................................. 49 3.4 REFERENCES............................................................................................................ 57

Chapter 4: Immunoadsorption Model for the VFPR ....................... 59 4.1 INTRODUCTION ...................................................................................................... 59 4.2 IMMUNOADSORPTIVE GEL................................................................................. 59

4.2.1 Solute Partitioning ............................................................................................... 59 4.2.2 Adsorption Isotherm............................................................................................ 60 4.2.3 Adsorption Site Distribution............................................................................... 61 4.2.4 Effective Diffusivity ............................................................................................. 62

4.3 DEVICE MODEL....................................................................................................... 62 4.3.1 Blood Compartment ............................................................................................ 62 4.3.2 Active Plasma Compartment (APC) .................................................................. 63 4.3.3 Plasma Line, Collection Chamber, and Blood Outlet Port.............................. 65

4.4 RESERVOIR MODEL............................................................................................... 65 4.5 CHARACTERIZATION OF MASS-TRANSFER TO THE SURFACE OF SUSPENDED PARTICLES............................................................................................. 66 4.6 COMPUTATIONAL METHODS............................................................................. 67 4.7 RESULTS AND DISCUSSION ................................................................................. 67 4.8 REFERENCES............................................................................................................ 78

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Chapter 5: ScFv-Based Immunoadsorbent .....................................79 5.1 INTRODUCTION ...................................................................................................... 79 5.2 METHODS.................................................................................................................. 79

5.2.1 Labeling of β2m .................................................................................................... 79 5.2.2 Cloning of VH and VL genes ................................................................................ 80 5.2.3 Display of scFv fragment by yeast...................................................................... 81

5.2.3.1 Insert Assembly ............................................................................................... 81 5.2.3.2 Plasmid Construction ..................................................................................... 82 5.2.3.3 Yeast Transformation, Growth, and Induction ............................................... 82 5.2.3.4 Yeast Labeling................................................................................................. 83 5.2.3.5 FACS Analysis ................................................................................................ 83 5.2.3.6 Mathematical Modeling .................................................................................. 84

5.2.4 Secretion of scFv fragment by yeast................................................................... 85 5.2.4.1 Plasmid Construction ..................................................................................... 85 5.2.4.2 Yeast Transformation, Growth, and Induction ............................................... 86 5.2.4.3 Protein Purification ........................................................................................ 87

5.2.5 Immunoadsorbent based on scFv fragment ...................................................... 87 5.2.5.1 Protein Immobilization ................................................................................... 87 5.2.5.2 Characterization ............................................................................................. 88

5.2.6 Statistical Analysis ............................................................................................... 90 5.3 RESULTS .................................................................................................................... 90

5.3.1 Cloning of VH and VL genes ................................................................................ 90 5.3.2 Display of scFv fragment by yeast...................................................................... 91 5.3.3 Secretion of scFv fragment by yeast................................................................... 91 5.3.4 Immunoadsorbent based on scFv fragment ...................................................... 91

5.4 DISCUSSION.............................................................................................................. 93 5.5 REFERENCES.......................................................................................................... 102

Chapter 6: Afterword.......................................................................105 6.1 SUMMARY AND CONCLUSIONS ....................................................................... 105 6.2 RECOMMENDATIONS FOR FUTURE WORK................................................. 110

6.2.1 Optimization of ScFv Production ..................................................................... 110 6.2.2 Optimization of ScFv Purification.................................................................... 111 6.2.3 Optimization of ScFv Immobilization.............................................................. 111

6.3 REFERENCES.......................................................................................................... 113

Appendix: Immunoadsorption Model FORTRAN 77 Program....... 115

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List of Figures Figure 1.1 Structural comparison of whole antibodies and single-chain variable region

antibody fragments (scFv)............................................................................................ 25

Figure 1.2 The Vortex Flow Plasmapheretic Reactor (VFPR). ........................................ 26

Figure 2.1 Diagram of the circuit used to study the clearance ββββ2m of from human blood. ......................................................................................................................................... 41

Figure 2.2 Dynamics of rββββ2m clearance from human blood with a BBM.1-loaded VFPR, in vitro............................................................................................................................. 41

Figure 3.1 Photograph of the new, larger VFPR prototype............................................. 53

Figure 3.2 Schematic diagram of the experimental setup used to obtain RTDs from the plasma port. ................................................................................................................... 54

Figure 3.3 The compartmental mixing model for the VFPR. .......................................... 54

Figure 3.4 Blood port residence time distribution functions for the small (top: a,b) and large (bottom: c,d) VFPR prototypes at plasma pump flowrates of 50 (left: a,c) and 100 (right: b,d) mL/min. ............................................................................................... 55

Figure 3.5 Plasma port RTD curves for the small (top: a,b) and large (bottom: c,d) VFPR prototypes at plasma pump flowrates of 50 (left: a,c) and 100 (right: b,d) mL/min........................................................................................................................... 56

Figure 4.1 Schematic diagram of the dynamic VFPR adsorption model. ...................... 71

Figure 4.2 Closed-loop blood detoxification with the VFPR. .......................................... 72

Figure 4.3 Apparatus used to conduct the dissolution studies......................................... 73

Figure 4.4 Equilibrium adsorption behavior of the immunoadsorptive media. ............ 74

Figure 4.5 Confocal micrograph of the immunoadsorptive gel: center cross-section of a typical bead (a) and an atypical bead (b).................................................................... 75

Figure 4.6 The predicted and observed dynamics of ββββ2m clearance from whole blood by an immunoadsorptive VFPR, in vitro.......................................................................... 76

Figure 4.7 Sensitivity analysis results for the model parameters km (a), R (b), De (c), and ΦΦΦΦ (d)................................................................................................................................ 77

Figure 5.1 Schematic diagram of yeast display. ................................................................. 97

Figure 5.2 Custom primers used for PCR. ......................................................................... 98

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Figure 5.3 VH and VL Genes Cloned from the BBM.1 Hybridoma.................................. 99

Figure 5.4 Titration of BBM.1-scFv displaying yeast with fluorescent β2m.................. 100

Figure 5.5 The scFv fragment secreted by YVH10 yeast transformed with pEAG3. .. 101

Figure 5.6 SDS-PAGE of the secreted BBM.1-scFv fragment after nickel affinity purification. ................................................................................................................. 101

Figure 6.1 Immunoadsorption model-predicted clearance of ββββ2m from whole blood by the large VFPR prototype loaded with the hypothetical scFv-based adsorbent.. . 109

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List of Tables Table 2.1 Capacity of the Immunoadsorptive Media ........................................................ 35

Table 2.2 Clearance of ββββ2m from Human Blood by the VFPR, In Vitro. ........................ 36

Table 2.3 Complete Blood Count Data for the BBM.1 VFPR Experiments (N=4)......... 37

Table 2.4 Total Protein Data for the VFPR BBM.1 Experiments and BSA Controls.... 37

Table 3.1 Comparison of the compartmental volumes of the two VFPR Prototypes.... 46

Table 3.2 Comparison of the pertinent length scales of the two VFPR Prototypes....... 46

Table 3.3 Model parameters calculated from the blood port RTD data for the small VFPR prototype. ........................................................................................................... 50

Table 3.4 Model parameters calculated from the blood port RTD data for the large VFPR prototype. ........................................................................................................... 50

Table 3.5 Model Parameters calculated from the plasma port RTD data for the small VFPR prototype. ........................................................................................................... 51

Table 3.6 Model Parameters calculated from the plasma port RTD data for the large VFPR prototype. ........................................................................................................... 52

Table 4.1 Model input parameters. .................................................................................... 69

Table 5.1 β2m-Adsorption Site Density of the Immunoadsorptive Media (ρ′′′′s). ............. 92

Table 6.1 Immunoadsorption model input parameters for the large VFPR prototype loaded with the hypothetical scFv-based adsorbent. ............................................... 108

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Chapter 1: Introduction 1.1 MOTIVATION

A frequent complication of end-stage renal disease (ESRD) is dialysis-related

amyloidosis (DRA), a debilitating disorder associated with the long-term accumulation of β2-

microglobulin (β2m) [Gejyo et al., 1985; Drueke, 2000]. Symptoms are caused by the

formation of amyloid deposits and include chronic pain, carpal tunnel syndrome, nerve

compressions, and cystic bone lesions with associated fractures. β2m, the primary

constituent of DRA amyloid, is a highly conserved globular protein (11.8 kD) that is secreted

by all nucleated cells and is specifically removed from the blood plasma by healthy kidneys.

Presently, there are no widely available treatments to prevent this chronic and debilitating

disease, short of a kidney transplant. Conventional kidney function replacement technologies

such as hemodialysis, hemodiafiltration, and peritoneal dialysis are believed to remove

insufficient quantities of β2m, as they are non-specific and based on size-exclusion [Ameer,

2001]. Even so, research has revealed a correlation between the removal of β2m from the

circulation and a delay in the occurrence of symptoms [Miyata et al., 1998; Drueke, 2000;

Lornoy et al., 2000]. In recent years, adsorbents that are based on hydrophobic adsorption

and size-exclusion (Lixelle® and Betasorb®) have been developed for the extracorporeal

removal of β2m [Furuyoshi et al., 1998; Davankov et al., 2000]. However, their specificity

and/or affinity for β2m remains in question, complicating the evaluation of patient outcome

due to their use [Tsuchida et al., 1998; Reiter et al., 2002; Tsuchida et al., 2002].

Ideally, an adsorbent material for the extracorporeal removal of β2m should be highly

specific, so as to prevent the significant loss of proteins and other molecules that are

beneficial to the patient. Furthermore, a highly specific β2m-adsorbent material could also

serve as a valuable tool for research. It could potentially be used to study the therapeutic

efficacy of β2m clearance independent of the removal of other molecules that have also been

implicated in the pathogenesis of DRA, such as inflammatory cytokines [Miyata et al., 1994;

Matsuo et al., 2000; Niwa, 2001]. The optimal β2m-adsorbent should possess an affinity for

β2m that is strong enough to bring the concentration to a level that is well below normal (1

mg/mL [Floege and Ketteler, 2001]). This high affinity would serve to increase the rate of

β2m removal from the patient by maximizing the concentration gradient that drives the mass-

20

transfer rate of β2m to the adsorption sites. Along these lines, the adsorbent material should

consist of small porous particles in order to minimize the time-scales of convective and

diffusive mass-transport.

Antibodies are a logical choice as the active species (or ligand) on which to base a

β2m-adsorbent material, as they can be highly specific and possess a high affinity for their

target molecules. In the past, antibodies immobilized onto small porous beads have been

used to clear β2m from human plasma [Mogi et al., 1989; Nakano et al., 1991; Vallar et al.,

1995; Shabunina et al., 2001]. However, this research did not address the challenge using of

small (i.e. 100 µm) immunoadsorptive particles for the removal of β2m from whole blood in

a clinically feasible system. It is necessary to perform plasmapheresis (the separation of

plasma from blood cells) before using small (< 400 µm) beads for the extracorporeal removal

of β2m because unacceptably high levels of blood cell lysis occur when packed beds of this

type are perfused with whole blood (direct hemoperfusion or DHP) under these conditions

[Furuyoshi et al., 1998]. While packed beds of relatively large (> 400 µm) beads (Lixelle®

and Betasorb® columns) have been safely used for this application [Furuyoshi et al., 1998;

Davankov et al., 2000], they possess inherent mass-transfer limitations. In fact, due to the

low surface area to volume ratio of such large particles, the rate of toxin removal is directly

proportional to the volume of adsorbent. Hence, increasing the volume of adsorbent used for

DHP can increase the rate of blood detoxification, but this comes at the expense of additional

blood hold-up (a biocompatibility issue). This is why the volumes of DHP columns used to

date (Lixelle® and Betasorb®) for the extracorporeal removal of β2m have been kept below

350 mL [Furuyoshi et al., 1998; Ronco et al., 2001].

As immunoadsorption ligands, single-chain variable region antibody fragments (scFv,

Figure 1.1) offer several potential advantages over whole polyclonal or monoclonal

antibodies. The transfer of antibody genes to a defined expression vector provides the

opportunity to eliminate the production of unwanted immunoglobulins. ScFv fragments are

also smaller in size, which should theoretically allow for higher effective β2m adsorption site

densities (steric argument). This would reduce the volume of adsorbent required for

therapeutic efficacy, thereby minimizing the retention of blood components during operation.

Additionally, the properties (affinity, stability, expression yield) of scFv fragments can be

engineered through in vitro evolution in a yeast display format [Boder and Wittrup, 1997;

21

Boder and Wittrup, 1998; Boder and Wittrup, 2000]. The fact that scFv fragments can be

produced through microbial expression vectors provides greater flexibility for the

optimization of the production process economics [Datar et al., 1993]. Furthermore, very

high yields (3.1 g-scFv/L-culture) of properly folded scFv fragments have been expressed in

and purified from the cytoplasm of E. coli [Martineau et al., 1998].

The Vortex Flow Plasmapheretic Reactor (VFPR, refer to Figure 1.2 and Section 1.3)

is a multi-compartment extracorporeal device that was originally developed to carry out the

safe and efficient enzymatic neutralization of heparin in whole blood [Ameer, Barabino et

al., 1999; Ameer, Raghavan et al., 1999]. The VFPR is the first device designed to use

Taylor vortices and a fluidized bed of particles to conduct a heterogeneous reaction or

adsorption process on whole blood. A major advantage of fluidized beds over packed beds is

that they exhibit lower pressure drops (when all other specifications are held constant) [Kunii

and Levenspiel, 1977]. The fluidized bed of the VFPR also possesses an unusually high

aspect ratio (length of the mesh divided by the radial distance between the membrane and

mesh), which also contributes to its low-pressure drop (generally less than 20 mmHg). Most

importantly, however, the compartmental design of the VFPR allows for the use of relatively

small (approximately 100 µm) active particles that possess inherent mass-transfer advantages

over larger ones. The relatively high surface area to volume ratio of these smaller particles

could potentially allow for a significant reduction in the volume of the adsorbent required for

the effective extracorporeal removal of β2m, which would represent an improvement in

biocompatibility.

The research presented herein investigates the feasibility of using the VFPR design

for the immunoadsorptive extracorporeal removal of β2m through experiments with whole

human blood, in vitro. Initially, immobilized whole monoclonal antibodies and a device

prototype are investigated as a model system. A mathematical model that describes the

dynamic behavior of the immunoadsorptive VFPR is presented that is intended to serve as a

design tool for future device prototypes, experiments, and potential clinical trials. Finally, a

new type of immunoadsorbent for the extracorporeal removal of β2m is developed that is

based upon scFv antibody fragments. The goal of this research is to lay a foundation for a

new extracorporeal β2m-removal technology that is more specific, biocompatible, and

effective than existing methods. Demonstrating the efficacy of this technology as a therapy

22

for DRA would support its tailored application for treating other pathologies that are caused

by circulating compounds such as sepsis, liver failure, autoimmune disease, drug overdoses,

and genetic disorders.

23

1.2 SPECIFIC AIMS

This thesis investigates feasibility of using the VFPR design with immobilized

antibodies for the extracorporeal removal of β2m as a potential therapy for DRA. More

specifically, this thesis aims to:

1. Evaluate the biocompatibility and efficacy of an immunoadsorptive VFPR for this

application through experimentation with recombinant human β2m, monoclonal

antibodies, and a reservoir of whole human blood, in vitro. Here, biocompatibility

will be assessed in terms of the effect that the immunoadsorptive device has on blood

components (complete cell count, total protein, and plasma free hemoglobin). The

efficacy of the device is defined as its ability to bring the β2m concentration down to

a level that is below the normal range of healthy individuals (1.0-3.0 mg/L [Floege

and Ketteler, 2001]) at a clinically relevant flowrate (on the order of 70 mL-

plasma/min, the approximate flowrate of extravascular β2m into the circulation

[Floege et al., 1991]).

2. Develop a mathematical model for the immunoadsorptive VFPR that is based upon

the independent characterization of the mass-transfer processes within the device and

the thermodynamic behavior of a model immunoadsorbent.

3. Create and characterize a novel β2m-adsorbent material that is based upon high-

affinity scFv antibody fragments and possesses a mass ratio of adsorbed β2m to

immobilized antibody that is at or above the theoretical limit for bivalent whole

antibodies (0.16 mg-β2m/mg-antibody). For this application, a high-affinity scFv

fragment is defined as one that has an equilibrium dissociation constant that is well

below the lower limit of β2m concentrations found in healthy individuals (KD << 1

mg-β2m/L ≈ 100 nM). Creating an immunoadsorbent with a high mass ratio of

adsorbed β2m to immobilized antibody (under saturating conditions) would support

the future development an immunoadsorbent with the highest β2m adsorption site

density reported to date (> 0.9 mg-β2m/mL-settled-gel [Vallar et al., 1995]).

24

1.3 THE VORTEX FLOW PLASMAPHERETIC REACTOR (VFPR)*

A VFPR is constructed by counter-boring two concentric chambers within the outer

cylinder wall of a Taylor-Couette vortex flow device (Figure 1.2). The collection chamber is

sealed with a polyester mesh filter (15 µm opening) to keep the fluidized bed of particles

within the active plasma chamber. These particles are typically gel beads that are

approximately 100 µm in diameter, are highly porous, and have the active species

immobilized onto them (i.e. an antibody or enzyme). The active plasma compartment is

sealed with a 1 µm pore-size, track-etched polyester membrane to prevent contact between

blood cells and the gel beads. Compartmentalization in this novel Taylor-Couette flow

device eliminates red cell lysis due to particle fluidization and prevents white cell and platelet

activation due to contact with the active gel beads [Ameer, Harmon et al., 1999].

During operation, whole blood is pumped into the inlet port (typically 200-400

mL/min) and channeled through the innermost annular, or �blood�, compartment. A

dedicated peristaltic pump (�plasma pump�) controls the plasma flowrate through the

microporous membrane, the active plasma compartment, and the plasma collection chamber

(typically 50-75 mL/min). The rotation of the solid inner cylinder (usually at about 1.2x103

rpm) is achieved via magnetic coupling and serves to create the Taylor vortices [Donnelly,

1991] in the blood compartment. These flow instabilities induce undulations throughout the

unsupported microporous membrane, fluidizing the gel beads in the active plasma

compartment. The cleansed plasma exits the active plasma compartment via the collection

chamber, which retains the gel beads. The cleansed plasma is returned to the top of the

device where it mixes with bypassed cells and plasma prior to exiting the VFPR via the blood

outlet port. These mechanisms enable the VFPR to perform high-flux plasmapheresis in

series with a fluidized bed reaction or adsorption process. The More detailed descriptions of

specific device prototypes are provided Chapters 2 and 3 of this document and have been

published elsewhere [Ameer, Barabino et al., 1999; Ameer, Raghavan et al., 1999].

* This section has appeared in a research article originally published in the AIChE Journal [Grovender et al., 2002]. It has been reproduced with permission of the American Institute of Chemical Engineers. Copyright © 2002 AIChE. All rights reserved.

25

Figure 1.1 Structural comparison of whole antibodies and single-chain variable region antibody fragments (scFv). Whole antibodies are approximately 150 kD, while scFv fragments are generally 25-30 kD. The scFv fragment shown is assembled in a VH-linker-VL configuration.

VH

VL

Antigen Binding Sites Antigen Binding Site

Linking Peptide

Whole Antibody ScFv Fragment

V LV H V

L

VH

VH

VL

VH

VL

Antigen Binding Sites Antigen Binding Site

Linking Peptide

Whole Antibody ScFv Fragment

V LV H V

L

VH

V LV H

V LV H V

L

VH V

L

VH

26

* This figure has been previously published in Kidney International [Ameer et al., 2001]. It has been used with permission from Blackwell Publishing. Copyright © 2001 Blackwell Publishing. All rights reserved.

Figure 1.2 The Vortex Flow Plasmapheretic Reactor (VFPR).* The whole blood path is shown in red, while the regions accessible only to plasma are shown in gold. The Taylor vortices in the blood compartment reduce the cell polarization layer formed at the surface of the membrane (allowing for higher blood filtration rates) and induce periodic undulations in the unsupported microporous membrane. These membrane undulations drive the mixing and fluidization of the active plasma compartment.

Bearing

RotatingInner

Cylinder

WholeBloodOutlet

Whole BloodInlet

Mesh

MicroporousMembrane

PlasmaPump

Blood Compartmentwith Taylor Vortices

ActivePlasma

Compartment

MediaInjection Port

PlasmaCollectionChamber

Plasma Line

27

1.4 REFERENCES Ameer GA (2001) "Modalities for the Removal of Beta-2-Microglobulin from Blood." Semin Dial. 14: 103-6.

Ameer GA, G Barabino, R Sasisekharan, W Harmon, CL Cooney and R Langer (1999) "Ex Vivo Evaluation of a Taylor-Couette Flow, Immobilized Heparinase I Device for Clinical Application." Proc Natl Acad Sci USA. 96: 2350-5.

Ameer GA, EA Grovender, H Ploegh, D Ting, WF Owen, M Rupnick and R Langer (2001) "A Novel Immunoadsorption Device for Removing Beta2-Microglobulin from Whole Blood." Kidney Int. 59: 1544-50.

Ameer GA, W Harmon, R Sasisekharan and R Langer (1999) "Investigation of a Whole Blood Fluidized Bed Taylor-Couette Flow Device for Enzymatic Heparin Neutralization." Biotechnol Bioeng. 62: 602-8.

Ameer GA, S Raghavan, R Sasisekharan, W Harmon, CL Cooney and R Langer (1999) "Regional Heparinization Via Simultaneous Separation and Reaction in a Novel Taylor-Couette Flow Device." Biotechnol Bioeng. 63: 618-24.

Boder ET and KD Wittrup (1997) "Yeast Surface Display for Screening Combinatorial Polypeptide Libraries." Nat Biotechnol. 15: 553-7.

Boder ET and KD Wittrup (1998) "Optimal Screening of Surface-Displayed Polypeptide Libraries." Biotechnol Prog. 14: 55-62.

Boder ET and KD Wittrup (2000) "Yeast Surface Display for Directed Evolution of Protein Expression, Affinity, and Stability." Methods Enzymol. 328: 430-44.

Datar RV, T Cartwright and CG Rosen (1993) "Process Economics of Animal Cell and Bacterial Fermentaions: A Case Study Analysis of Tissue Plasminogen Activator." Bio-Technology. 11: 349-57.

Davankov V, L Pavlova, M Tsyurupa, J Brady, M Balsamo and E Yousha (2000) "Polymeric Adsorbent for Removing Toxic Proteins from Blood of Patients with Kidney Failure." J Chromatogr B Biomed Sci Appl. 739: 73-80.

Donnelly R (1991) "Taylor-Couette Flow: The Early Days." Physics Today. 44: 32-9.

Drueke TB (2000) "Beta-2-Microglobulin and Amyloidosis." Nephrol Dial Transplant. 15: 17-24.

Floege J, A Bartsch, M Schulze, S Shaldon, KM Koch and LC Smeby (1991) "Clearance and Synthesis Rates of Beta-2-Microglobulin in Patients Undergoing Hemodialysis and in Normal Subjects." J Lab Clin Med. 118: 153-65.

Floege J and M Ketteler (2001) "Beta-2-Microglobulin-Derived Amyloidosis: An Update." Kidney Int. 59 Suppl 78: S164-71.

Furuyoshi S, M Nakatani, J Taman, H Kutsuki, S Takata and N Tani (1998) "New Adsorption Column (Lixelle) to Eliminate Beta-2-Microglobulin for Direct Hemoperfusion." Ther Apher. 2: 13-7.

Gejyo F, T Yamada, S Odani, Y Nakagawa, M Arakawa, T Kunitomo, H Kataoka, M Suzuki, Y Hirasawa, T Shirahama and et al. (1985) "A New Form of Amyloid Protein Associated with Chronic Hemodialysis Was Identified as Beta 2-Microglobulin." Biochem Biophys Res Commun. 129: 701-6.

28

Grovender EA, CL Cooney, R Langer and GA Ameer (2002) "Immunoadsorption Model for a Novel Fluidized-Bed Blood Detoxification Device." AIChE Journal. 48: 2357-65.

Kunii D and O Levenspiel (1977) Fluidization Engineering, Robert E. Krieger Publishing Company, Huntington, New York.

Lornoy W, I Becaus, JM Billiouw, L Sierens, P Van Malderen and P D'Haenens (2000) "On-Line Haemodiafiltration. Remarkable Removal of Beta-2-Microglobulin. Long-Term Clinical Observations." Nephrol Dial Transplant. 15 Suppl 1: 49-54.

Martineau P, P Jones and G Winter (1998) "Expression of an Antibody Fragment at High Levels in the Bacterial Cytoplasm." Journal of Molecular Biology. 280: 117-27.

Matsuo K, TA Ikizler, RL Hoover, M Nakamoto, C Yasunaga, LB Pupim and RM Hakim (2000) "Transforming Growth Factor-Beta Is Involved in the Pathogenesis of Dialysis-Related Amyloidosis." Kidney International. 57: 697-708.

Miyata T, R Inagi, Y Iida, M Sato, N Yamada, O Oda, K Maeda and H Seo (1994) "Involvement of Beta(2)-Microglobulin Modified with Advanced Glycation End-Products in the Pathogenesis of Hemodialysis-Associated Amyloidosis - Induction of Human Monocyte Chemotaxis and Macrophage Secretion of Tumor-Necrosis-Factor-Alpha and Interleukin-1." Journal of Clinical Investigation. 93: 521-8.

Miyata T, M Jadoul, K Kurokawa and C Van Ypersele de Strihou (1998) "Beta-2-Microglobulin in Renal Disease." J Am Soc Nephrol. 9: 1723-35.

Mogi M, M Harada, T Adachi, K Kojima and T Nagatsu (1989) "Selective Removal of Beta-2-Microglobulin from Human Plasma by High-Performance Immunoaffinity Chromatography." J Chromatogr B Biomed Sci Appl. 496: 194-200.

Nakano H, H Gomi, T Shibasaki, F Ishimoto and O Sakai (1991) "An Experimental Study on Selective Elimination of Beta-2-Microglobulin Using Immunoadsorption Method in Patients with Chronic Renal Failure." Biomater Artif Cells Immobilization Biotechnol. 19: 61-9.

Niwa T (2001) "Dialysis-Related Amyloidosis: Pathogenesis Focusing on Age Modification." Semin Dial. 14: 123-6.

Reiter K, V Bordoni, G Dall'Olio, MG Ricatti, M Soli, S Ruperti, G Soffiati, E Galloni, V D'Intini, R Bellomo and C Ronco (2002) "In Vito Removal of Therapeutic Drugs with a Novel Adsorbent System." Blood Purification. 20: 380-8.

Ronco C, A Brendolan, JF Winchester, E Golds, J Clemmer, HD Polaschegg, TE Muller, G La Greca and NW Levin (2001) "First Clinical Experience with an Adjunctive Hemoperfusion Device Designed Specifically to Remove Beta-2-Microglobulin in Hemodialysis." Blood Purification. 19: 260-89.

Shabunina IV, OI Afanas'eva and SN Pokrovskii (2001) "Immunosorbent for Removal of Beta-2-Microglobulin from Human Blood Plasma." Bulletin of Experimental Biology and Medicine. 4: 984-6.

Tsuchida K, Y Takemoto, T Nakamura, O Fu, C Okada, S Yamagami and T Kishimoto (1998) "Lixelle Adsorbent to Remove Inflammatory Cytokines." Artif Organs. 22: 1064-7.

Tsuchida L, Y Takemoto, K Sugimura, R Yoshimura, K Yamamoto and T Nakatani (2002) "Adsorption of Endotoxin by Beta(2)-Microglobulin Adsorbent Column (Lixelle): The New Approach for Endotoxinemia." Therapeutic Apheresis. 6: 116-8.

29

Vallar L, PM Costa, A Teixeira, M Pfister, R Barrois, PP Costa and C Rivat (1995) "Immunoadsorption Procedure as a Potential Method for the Specific Beta 2-Microglobulin Removal from Plasma of Patients with Chronic Renal Failure." J Chromatogr B Biomed Appl. 664: 97-106.

31

Chapter 2: In Vitro Removal of ββββ2-Microglobulin from Human Blood with an Immunoadsorptive VFPR* 2.1 INTRODUCTION

High plasma levels of β2-microglobulin (β2m) have been implicated in the formation

of the severely destructive and potentially fatal amyloid deposits that are characteristic of

dialysis-related amyloidosis (DRA) [Gejyo et al., 1985; Drueke, 2000]. Conventional renal

replacement technologies remove insufficient quantities of β2m to normalize plasma levels

[Ameer, 2001]. This limitation arises due to non-specific adsorptive qualities and reliance on

size exclusion, which can also remove other middle molecular weight proteins. These non-

specific approaches also make it difficult to evaluate the role and contribution of middle

molecular weight molecules to the pathology of DRA and other morbidities of end stage

renal disease. A high affinity and biologically specific approach could target a protein,

prevent significant loss of other important molecules, and improve the apparent adsorption

rate within an extracorporeal device. This chapter describes the use of agarose-immobilized

murine anti-human β2m monoclonal antibodies in a Vortex Flow Plasmapheretic Reactor

(VFPR) to remove donor baseline and controlled amounts of human β2m from human blood

in vitro.

2.2 METHODS

2.2.1 Assays

Serum and plasma β2m concentrations were assayed with the β2-micro RIA

(radioimmunoassay) kit available from Pharmacia-Upjohn (MI), while the buffer β2m

concentrations were determined by using an extinction coefficient of 20,065 M-1 cm-1 at 280

nm. This value was derived from the published amino acid sequence of human β2m [Suggs

et al., 1981] and the equation reported by Pace and co-workers [Pace et al., 1995]. Bradford

protein assays were performed according to the dye manufacturer�s instructions (Bio-Rad,

CA), using a bovine gamma globulin standard (Pierce, IL). Plasma free hemoglobin assays

were performed according to the instructions of a kit purchased from Sigma Chemical (MO).

* This chapter is a revised version of a research article previously published in Kidney International [Ameer et al., 2001]. It has been used with permission from Blackwell Publishing. Copyright © 2001 Blackwell Publishing. All rights reserved.

32

Complete blood counts and total protein assays were performed at the MIT Medical

Laboratory.

2.2.2 Protein Immobilization

BBM.1 monoclonal antibody (hybridoma purchased as ATCC HB-28) [Brodsky et

al., 1979; Parham et al., 1983] and bovine serum albumin (BSA) were each immobilized

onto 48 mL settled-volumes of Sepharose CL-4B agarose gel beads (Amersham-Pharmacia,

Sweden) using a modified version of a method previously described [Cuatrecasas et al.,

1968].

The gel beads were rinsed with 1 L of ultrapurified water, and then combined with 50

mL of ultrapurified water and 100 mL of 2 M sodium carbonate. After being chilled on ice,

the agarose gel suspension was activated for 5 minutes with 20% w/v cyanogen bromide

(each gram pre-dissolved in 1.5 mL acetonitrile). The activated gel was rinsed sequentially

with 1 L of each of the following ice-chilled fluids: ultrapurified water, 1 mM hydrochloric

acid, and bicarbonate buffer (0.5 M sodium chloride, 0.1 sodium bicarbonate, pH 8.3). The

fluid in the gel void volume was removed and the activated agarose was combined with the

protein to be immobilized (167 mg of BBM.1 via Bradford dye assay and 174 mg BSA by

dry weight) in 82 mL of phosphate buffered saline, pH 7.4 (PBS). The protein was allowed

to bind to the activated agarose suspension for 40 hours at 4OC with gentle mixing. The

buffer was removed from the agarose gel and assayed for its residual protein concentration

(Bradford assay for BBM.1 and change in absorbance at 280 nm for BSA). The activated gel

was quenched by mixing it with a lysine buffer (0.2 M lysine, 0.5 M sodium chloride, 0.1 M

sodium bicarbonate, pH 8.3) for one hour at 4OC. The gel was rinsed quickly with 500 mL

PBS and rinsed overnight with 200 mL PBS at 4OC. The following day, the overnight rinse

was replaced with fresh PBS. A sample was incubated for one hour at 37 OC to check the

thermal stability of the immobilized protein (Bradford assay). Coomassie stained SDS-

PAGE was used to check for protein in the lysine quenching buffer and PBS rinses.

2.2.3 Recombinant ββββ2m Preparation

The β2m E. coli expression vector [Garboczi et al., 1992] was a generous gift from

the Wiley Laboratory (Cambridge, MA) and the recombinant protein was produced in a

33

fashion similar to those previously described [Buchner and Rudolph, 1991; Fan et al., 1996].

Each liter of Luria-Bertani medium (fortified with 0.4% w/v glucose and 0.100 mg/mL

ampicillin) was inoculated with frozen stock, incubated at 37OC, and induced with 0.5 mM

isopropyl β-D-thiogaloctopyranoside during the log growth phase. The bacteria was

centrifuged at 5k x g for 20 minutes and resuspended in 50 mM Tris-HCl, 25% w/v sucrose,

1 mM sodium ethylenediaminetetraacetic acid (EDTA), 10 mM dithiothreitol (DTT), pH 8.0.

Cell lysis and DNA degradation were effected through the addition of 1 mg/mL lysozyme,

0.1 mg/mL DNase I (Sigma DN-25), 5 mM magnesium chloride, 1% Triton X-100, 1%

sodium deoxycholate, 10 mM DTT, and 70 mM sodium chloride. The insoluble protein was

rinsed several times with 50 mM Tris-HCl, 100 mM sodium chloride, 1 mM EDTA, 0.5%

Triton X-100, 1 mM DTT, pH 8.0 and one final time with 50 mM Tris-HCl, 1mM EDTA, pH

8.0. The washed inclusion body protein was solubilized in 8 M urea, 25 mM 2-[N-

morpholino]ethanesulfonic acid (MES), 10 mM EDTA, 0.1 mM DTT, pH 6.0 and

ultracentrifuged for 30 minutes at 25OC and 186,000 x g. The denatured protein was refolded

through dilution into 100 mM Tris-HCl, 400 mM L-arginine-HCl, 2 mM EDTA, 0.5 mM

oxidized glutathione, 5 mM reduced glutathione, pH 8.0. The refolded β2m was purified via

size-exclusion chromatography using prep-grade Superose® 12 resin (Amersham-

Pharmacia), eluted with 20 mM Tris-HCl, 150 mM sodium chloride, pH 8.0. In order to

remove residual refolding buffer, the β2m was dialyzed against the elution buffer with a 6-8

kD membrane (Spectrum Laboratories, CA).

2.2.4 Capacity of the Immunoadsorptive Media

Porcine serum, loaded with three different saturating concentrations of rβ2m, was

used to quantify the capacity of the immunoadsorptive media. Briefly, 10 mL of 50%

gel/PBS suspension, 30 mL of 5 micron-filtered Porcine serum (GIBCO BRL, MD), and

either 0.23, 0.31, or 0.40 mg of rβ2m (stock: 0.94 ± 0.02 mg/mL in elution buffer) were

combined in 50 mL polypropylene tubes (Corning, NY). The tubes were equilibrated under

well-mixed conditions for at least 1 hour at 37OC. The rβ2m-adsorptive capacity of the

agarose-immobilized monoclonal antibody was calculated using Equation 2.1, where ρ′s is

the adsorption site density on a settled bed volume basis (mg-rβ2m/L-settled-gel), Vtotal is the

total volume of the system (mL), Vgel is the settled-volume of gel (mL), C0 is the initial

34

diluted concentration of rβ2m in the system (mg/L), and Ceq is the equilibrium concentration

of desorbed rβ2m (mg/L).

( )0total

s eqgel

V C CV

ρ′ = − [2.1]

2.2.5 Clearance of ββββ2m from Whole Blood by a VFPR in a Closed-Loop Circuit

The MIT Committee on the Use of Humans as Experimental Subjects approved all

experiments with human blood. Healthy, volunteer blood donors read and signed informed

consent forms. The staff at the Children’s Hospital Blood Donor Center (Boston, MA)

performed the phlebotomies. Each donation (450 mL nominal volume) was used the same

day it was received and had 63 mL of citrate phosphate dextrose adenine solution added as an

anti-coagulant (Baxter, IL). The VFPR and circuit tubing were primed with 0.9% w/v

sodium chloride (USP grade, Abbott Laboratories, IL) and the agarose gel was injected into

the adsorptive compartment. The blood bag was placed on a shaker and connected to the

VFPR in a closed-loop circuit (Figure 2.1). Before the plasma pump and VFPR cylinder

were turned on, the main circuit pump was run for 5 minutes to mix the blood with the saline

outside of the plasma chambers and plasma line. During the first 60 minutes of a two-hour

hemoperfusion, the native donor β2m was cleared from the circuit by running the plasma

pump and the inner VFPR cylinder. Samples were taken before and after this period, and the

adsorptive chamber was flushed with 0.9% w/v sodium chloride (BBM.1 gel only).

The immunoadsorptive media (but not the BSA gel) was regenerated with 1.5 L of

0.3 M glycine-HCl, pH 2.8. The regenerated BBM.1 gel was rinsed with 1.5 L of PBS and

re-injected into the adsorptive chamber of the VFPR. Recombinant human β2m (1.5 mg in

elution buffer) was injected into the circuit, allowed to mix with the blood for 5 minutes, and

samples were taken. The recombinant β2m was cleared from the circuit by turning on the

plasma pump and VFPR cylinder. Samples were taken over a period of 60 minutes and the

media was regenerated as before (both BBM.1 and BSA). The samples collected were

assayed for their total protein, plasma free hemoglobin, complete blood count, and β2m

concentration. System efficacy was quantified by calculating the conversion of β2m

adsorption, Xadsorption, as shown by Equation 2.2 (dimensionless). Here M initial and Mfinal are

the initial and final masses (mg) of desorbed β2m in the system, respectively.

35

initial

finaladsorption M

M1X −= [2.2]

2.2.6 Statistical Analysis

Observed variables are reported as the mean ± SEM (standard error of the mean). All

experiments were performed in triplicate (N=3), unless otherwise noted. Analysis of

variance (ANOVA) was used to determine the significance of the differences among three or

more means, while the student�s two-sample t-test was used to compare pairs of means. The

criterion for significance was a two-tailed p-value of 0.05.

2.3 RESULTS

2.3.1 Protein Immobilization

Most of the BBM.1 (92%) and the BSA (97%) bound to the activated agarose gel,

yielding immobilization densities of 3.0 and 3.5 mg/mL-settled-gel, respectively. The lysine

quenching buffer and the PBS rinses did not show significant amounts of BBM.1 on SDS-

PAGE as compared to equal volume samples of BBM.1 in PBS from before and after

activated substrate contact. Protein leaching, after 1 hour of 37OC incubation, in the BBM.1

and BSA 1 samples was found to be only 2.9 ± 0.7 and 0.5 ± 0.2 mg/L-PBS, respectively.

2.3.2 Capacity of the Immunoadsorptive Media

Table 2.1 shows the results from the adsorption capacity measurements. The rβ2m

binding capacity of the immunoadsorptive media, ρ′s, was calculated to be 30 ± 2 mg-rβ2m

/L-settled-gel. Assuming bivalent BBM.1-β2m binding, this value corresponds to a BBM.1

efficiency of 6%. There was no apparent effect of the 0.3 M glycine stripping buffer on the

binding capacity.

Initial Concentration C0 [mg/L, N=4]

Final Concentration Ceq [mg/L]

Binding Site Density ρρρρ′′′′ s [mg-ββββ2m/L-settled-gel]

5.8 ± 0.1 2.1 ± 0.0 30. ± 0.

7.7 ± 0.2 3.8 ± 0.2 32. ± 1.

10. ± 0. 6.4 ± 0.3 29. ± 2.

Table 2.1 Capacity of the Immunoadsorptive Media

36

2.3.3 Clearance of ββββ2m from Human Blood with an Immunoadsorptive VFPR

The average total volume, native β2m concentration, and hematocrit of the

anticoagulated human blood was 529 ± 6 mL, 1.3 ± 0.1 mg/L, and 0.38 ± 0.01, respectively

(N=7). The final native β2m concentration of the BSA circuit was 0.5 ± 0.0 mg/L, while that

of the BBM.1 circuit was below detectable limits. Table 2.2 presents the observed native and

recombinant β2m adsorption conversions for the BBM.1 antibody and BSA control protein

matrices. The dynamics of rβ2m removal by the VFPR, loaded with BBM.1 gel, are

illustrated by Figure 2.2. The relatively low plasma line concentration (< 0.4 mg/L) indicates

that the apparent β2m adsorption rate within the plasma chamber was not limiting.

Furthermore, the time-scale of β2m clearance from the blood bag was in agreement with that

obtained by dividing the total blood path volume (445 mL) by the plasma flow rate (50

mL/min). The initial and final recombinant β2m concentrations in the BBM.1 circuit were

3.2 ± 0.2 and 0.2 ± 0.1 mg/L, respectively. This observed initial value was in agreement with

the value (3.4 mg/L) predicted by dividing the mass of injected rβ2m (1.5 mg) by the cell-free

volume of the blood bag, circuit tubing, and VFPR blood chamber (445 mL). The mass of

rβ2m adsorbed by the BBM.1 was 28 ± 2 mg/L-gel (settled volume), which was not

significantly different from the value of ρ′s measured a priori.

Native Recombinant

Minitial [mg]

Mfinal [mg] Xadsorption Minitial

[mg] Mfinal [mg] Xadsorption

BBM.1 [g] (N=4) 0.48±0.07 * 100%±6% 1.43±0.08 0.10±0.02 92%±2%

BSA [g] (N=3) 0.37±0.04 0.26±0.01 29%±6% 1.80±0.05 1.89±0.11 *

Significance p>0.05 p<0.002 p<0.0005 p < 0.02 � �

Table 2.3 and Table 2.4 report the effects of the VFPR circuit on cellular blood

elements and total protein, respectively. The donor bag plasma free hemoglobin level (HbP)

* Below detectable limits. � Values were not compared due to the significant difference in the initial conditions.

Table 2.2 Clearance of ββββ2m from Human Blood by the VFPR, In Vitro.

37

was 4.3 ± 1.1 mg/dL, while HbP at the end of native β2m removal (1 hour) was 8.9 ± 2.2

g/dL. This increase corresponded to 0.33 mg/dL per circuit pass. A HbP of 0.6 mg/dL per

pass through a hemodialyzer is generally considered acceptable [Ameer, Barabino et al.,

1999].

Native Recombinant

Diluted Bag* Initial Final Initial Final

Erythorcyte [M/µµµµL]� 3.39±0.08 3.23±0.20 3.26±0.08 3.18±0.11 3.51±0.15

Leukocyte [k/µµµµL]� 4.2±0.5 4.2±0.5 3.9±0.5 4.0±0.5 4.3±0.5

Platelet [k/µµµµL]� 164±13 175±15 162±13 161±18 172±20

Native Recombinant

Bag Initial Final Initial Final

BBM.1 (N=4)� 19.3±0.4 18.1±0.5 19.7±1.4 14.8±0.4 15.8±0.3

BSA (N=3)§ 19.1±0.5 17.7±0.4 18.5±0.54 ** 19.7±0.6

Significance�� p>0.8 p>0.5 p>0.5 N.A. p<0.005

* Values were not compared due to the significant difference in the initial conditions. Concentrations determined by multiplying the donor blood bag measurement by the dilution factor resulting from the saline priming volume. � No significant differences were found among the mean observed values for each count type over the two hour period (ANOVA, p>0.4). � No significant differences were found among the mean observed values during the native phase (ANOVA, p>0.4). A significant decrease was found between the native and recombinant phases (ANOVA, p<0.001), which was due to the flushing of the adsorptive compartment and the regeneration of the media. § No significant differences were found among the mean observed values (ANOVA, p>0.1). ** This sample was equivalent to the "Final Native" sample because the BSA gel was not regenerated. �� Two-sample t-test.

Table 2.3 Complete Blood Count Data for the BBM.1 VFPR Experiments (N=4).

Table 2.4 Total Protein Data for the VFPR BBM.1 Experiments and BSA Controls.

38

2.4 DISCUSSION

Although the clinical pathology of DRA is not fully understood, it has been shown

that removal of β2m can apparently delay the onset of the disease and improve symptoms

[Furuyoshi et al., 1998; Drueke, 2000; Lornoy et al., 2000]. For the first time, we have

shown the feasibility of removing β2m from whole blood within a single device via

immunoadsorption. As a first step, agarose-immobilized murine anti-human β2m

monoclonal antibodies (BBM.1) were used in a Vortex Flow Plasmapheretic Reactor (VFPR)

to remove both native and recombinant human β2m from human blood, in vitro. The

characteristics and advantages of the VFPR have been previously shown for the enzymatic

neutralization of heparin, to potentially make heparin anticoagulation during open-heart

surgery and dialysis safer [Bernstein et al., 1987; Leaver et al., 1992; Ameer, Barabino et al.,

1999]. Porous agarose gel beads were suspended within the adsorptive/reactive compartment

and did not come into contact with the blood cells, thereby minimizing hemolysis. The

agarose gel beads used in this study were hydrophilic and did not have any significant net

surface charge, which could result in ion exchange phenomena. Furthermore, the common

use of agarose gel beads in size exclusion chromatography also reflects its low protein-

binding characteristic. Our results demonstrated that a VFPR is able to clear low

concentrations of β2m from whole blood at a clinically relevant flow rate, without any

deleterious effects on the cellular blood components, total protein, or plasma free

hemoglobin. Other factors, such as complement activation could potentially be an issue with

agarose gel beads. However, the immobilization chemistry and support used in the study was

a model system to establish feasibility. The ability of the VFPR to perform adsorption,

without a separate plasma filter, should potentially render the device convenient for use

during dialysis. Furthermore, the relatively low whole blood priming volume of 50 mL

should minimize hemodilution.

Our approach offers several potential advantages. The VFPR design overcomes the

hemolysis and mass-transfer limitations associated with fluidized and packed columns when

they are used for direct hemoperfusion [Ameer, Harmon et al., 1999]. The high affinity of

the antibodies could potentially reduce patient β2m concentrations below those obtainable

with a low-affinity, hydrophobic adsorbent. The larger β2m-concentration difference

between the plasma and the adsorptive surface should result in an apparent increased rate of

39

adsorption. The high specificity of the antibodies should avoid the indiscriminate loss of

desirable molecules. In addition, immunoadsorption could potentially be used in clinical

trials as a diagnostic tool to help determine whether or not β2m clearance is the underlying

mechanism responsible for the therapeutic response of non-specific treatments. Some

investigators have shown that a hydrophobic adsorbent, thought to be selective for β2m,

removed various cytokines [Tsuchida et al., 1998]. Therefore, defined immunoadsorbents

could be targeted towards these molecules to help understand their role in the pathogenesis of

DRA or other morbidities associated with ESRD.

It is very difficult, and at times not practical, to reproduce in vitro all of the

parameters that are characteristic of an in vivo or ex vivo situation. Pathologic β2m levels and

larger β2m distribution volumes were not tested due to the limited available quantities of the

BBM.1 monoclonal antibody. However, the dynamics of β2m removal from blood with the

VFPR using the immobilized BBM.1 antibody as a model system could be evaluated. The

lower than expected immobilization yield of BBM.1 using the CNBr activated agarose beads

was also observed with agarose immobilized protein A, which specifically binds the Fc

region of an IgG antibody. This phenomenon could potentially be attributed to the expression

of an additional immunoglobulin (impurity) in the hybridoma culture, or simply an inherent

inability of immobilized BBM.1 to retain its binding activity. Even though our initial β2m

concentrations were relatively low, the adsorption kinetics of our system should not be

negatively affected by higher initial β2m concentrations. Provided a high-capacity

immunoadsorbent media is used, β2m concentrations that are characteristic of ESRD should

be cleared. Vallar and co-workers have reported high immobilization efficiencies (67%, ρ′s

= 0.9 mg-β2m/mL-settled-gel) of other Sepharose® CL-4B-immobilized anti-human β2m

monoclonal antibodies [Vallar et al., 1995]. A VFPR containing an immunoadsorbent media

of 0.9 mg-β2m/mL-settled-gel should remove clinically relevant quantities of β2m within the

allotted treatment time. A VFPR containing 300 mL of gel is potentially capable of

removing 270 mg of β2m. Depending on the initial plasma β2m levels, session duration, and

the type of dialysis membrane used, up to 250 mg β2m /session can be removed via filtration

and non-specific adsorption (about 100 mg/4-hr-session on average) [van Ypersele de

Strihou et al., 1994]. However, the key difference is the high affinity and specificity of

40

immunoadsorption. High affinity is important because it helps maintain a high apparent

adsorption rate within the VFPR.

To date, the emphases of attention to remove β2m from blood under clinically

relevant conditions have been filtration and hydrophobic interactions between the β2m and

the adsorptive media [Furuyoshi et al., 1998; Kay, 1999; Davankov et al., 2000; Drueke,

2000]. However, the specificity and affinity of these approaches continue to be a concern.

We overcame these obstacles by using monoclonal antibody technology. The BBM.1

antibody, produced by mammalian cell culture, had the required affinity to lower β2m

concentrations below the detectable limit of the radioimmunoassay. We anticipate that this

kind of affinity and specificity can be obtained using single chain antibody fragments (scFv)

[Raag and Whitlow, 1995], which offer several potential advantages over whole antibodies

(refer to Section 1.1). Future research will focus on the development of anti-β2m scFv

fragments and various immobilization chemistries to achieve a higher β2m binding site

density. Furthermore, the efficacy of the VFPR suggests that this technology could be

tailored for the treatment of a range of pathologies characterized by elevated circulating

concentrations of unwanted compounds, such as genetic disorders, liver failure, autoimmune

disease, sepsis, or drug overdoses.

41

Figure 2.1 Diagram of the circuit used to study the clearance ββββ2m of from human blood. The whole blood path is shown in red, while regions accessible only to plasma are shown in gold. The overall circulation flow rate was set at 200 mL/min, the plasma pump was calibrated to 50 mL/min, and the rotation rate was set at 1150 rpm. The volume of the tubing running from the blood bag to the VFPR was 60 mL, while the return tubing was 5 mL. The total reactor volume was 125 mL, which was distributed among the whole blood, adsorptive plasma, and plasma collection chambers as 50, 70, and 5 mL, respectively. The volume of the plasma tubing was 10 mL. The settled-volume of agarose gel beads was 48 mL. The blood temperature at the VFPR inlet and outlet was 35OC during the clearance of rβ2m. The dimensions of this device prototype are given in Section 3.2.1.

Figure 2.2 Dynamics of rββββ2m clearance from human blood with a BBM.1-loaded VFPR, in vitro. Error bars represent the standard error of the mean (SEM, N=4).

ShakerTable

SamplePort

rβ2mInjection

PortSample

Port

MainPump

Heater

VFPR

Blood Bag

0.0

1.0

2.0

3.0

4.0

0 10 20 30 40 50 60Time, minutes

Blood Bag

Plasma Line

ββ ββ 2m

Con

cent

ratio

n, m

g/L

42

2.5 REFERENCES Ameer GA (2001) "Modalities for the Removal of Beta-2-Microglobulin from Blood." Semin Dial. 14: 103-6.

Ameer GA, G Barabino, R Sasisekharan, W Harmon, CL Cooney and R Langer (1999) "Ex Vivo Evaluation of a Taylor-Couette Flow, Immobilized Heparinase I Device for Clinical Application." Proc Natl Acad Sci USA. 96: 2350-5.


Ameer GA, W Harmon, R Sasisekharan and R Langer (1999) "Investigation of a Whole Blood Fluidized Bed Taylor-Couette Flow Device for Enzymatic Heparin Neutralization." Biotechnol Bioeng. 62: 602-8.

Bernstein H, VC Yang, D Lund, M Randhawa, W Harmon and R Langer (1987) "Extracorporeal Enzymatic Heparin Removal: Use in a Sheep Dialysis Model." Kidney Int. 32: 452-63.

Brodsky FM, WF Bodmer and P Parham (1979) "Characterization of a Monoclonal Anti-Beta-2-Microglobulin Antibody and Its Use in the Genetic and Biochemical Analysis of Major Histocompatibility Antigens." Eur J Immunol. 9: 536-45.

Buchner J and R Rudolph (1991) "Renaturation, Purification and Characterization of Recombinant Fab-Fragments Produced in Escherichia Coli." Bio/Technology. 9: 157-61.

Cuatrecasas P, M Wilchek and CB Anfinsen (1968) "Selective Enzyme Purification by Affinity Chromatography." Proc Natl Acad Sci USA. 61: 636-43.


Drueke TB (2000) "Beta-2-Microglobulin and Amyloidosis." Nephrol Dial Transplant. 15: 17-24.

Fan QR, DN Garboczi, CC Winter, N Wagtmann, EO Long and DC Wiley (1996) "Direct Binding of a Soluble Natural Killer Cell Inhibitory Receptor to a Soluble Human Leukocyte Antigen-Cw4 Class I Major Histocompatibility Complex Molecule." Proc Natl Acad Sci USA. 93: 7178-83.


Garboczi DN, DT Hung and DC Wiley (1992) "Hla-A2-Peptide Complexes: Refolding and Crystallization of Molecules Expressed in Escherichia Coli and Complexed with Single Antigenic Peptides." Proc Natl Acad Sci USA. 89: 3429-33.

Gejyo F, T Yamada, S Odani, Y Nakagawa, M Arakawa, T Kunitomo, H Kataoka, M Suzuki, Y Hirasawa, T Shirahama and et al. (1985) "A New Form of Amyloid Protein Associated with Chronic Hemodialysis Was Identified as Beta 2-Microglobulin." Biochem Biophys Res Commun. 129: 701-6.

Kay J (1999) In Dialysis and Transplantation(Ed, Owen WD Jr, PB, Sayegh MH) WB Saunders Company, Philadelphia: pp. 237-52.

Leaver G, JA Howell and JR Conder (1992) "Adsorption Kinetics of Albumin on a Cross-Linked Cellulose Chromatographic Ion Exchanger." J Chromatog. 509: 101.

43

Lornoy W, I Becaus, JM Billiouw, L Sierens, P Van Malderen and P D'Haenens (2000) "On-Line Haemodiafiltration. Remarkable Removal of Beta-2-Microglobulin. Long-Term Clinical Observations." Nephrol Dial Transplant. 15 Suppl 1: 49-54.

Pace CN, F Vajdos, L Fee, G Grimsley and T Gray (1995) "How to Measure and Predict the Molar Absorption Coefficient of a Protein." Protein Sci. 4: 2411-23.

Parham P, MJ Androlewicz, NJ Holmes and BE Rothenberg (1983) "Arginine 45 Is a Major Part of the Antigenic Determinant of Human Beta-2-Microglobulin Recognized by Mouse Monoclonal Antibody Bbm.1." J Biol Chem. 258: 6179-86.

Raag R and M Whitlow (1995) "Single-Chain Fvs." Faseb J. 9: 73-80.

Suggs SV, RB Wallace, T Hirose, EH Kawashima and K Itakura (1981) "Use of Synthetic Oligonucleotides as Hybridization Probes: Isolation of Cloned Cdna Sequences for Human Beta-2-Microglobulin." Proc Natl Acad Sci USA. 78: 6613-7.



van Ypersele de Strihou C, J Floege, M Jadoul and KM Koch (1994) "Amyloidosis and Its Relationship to Different Dialysers." Nephrol Dial Transplant. 9 Suppl 2: 156-61.

45

Chapter 3: Macroscopic Mixing Model for the VFPR* 3.1 INTRODUCTION

Effective extracorporeal removal of β2m from a patient will require the VFPR to

exhibit favorable mass-transfer rates and to possess a sufficient binding capacity for β2m (up

to 500 mg). An accurate description of the macroscopic mixing pattern within the active

plasma compartment (APC) of the VFPR is required if the mass-transfer characteristics of

the fluidized particles are to be understood. A macroscopic mixing model, previously

developed to characterize the enzymatic degradation of heparin in the VFPR [Ameer et al.,

1999], has been unable to accurately describe the β2m-immunoadsorption data presented in

Chapter 2. Therefore, in this chapter, improved experimental methods and mathematical

analyses are presented which provide a better understanding of the macroscopic mixing

pattern within the VFPR. These methods are used to characterize the mixing behavior of the

prototype studied in Chapter 2 and a new, larger VFPR prototype. By comparing the results

from the two different device prototypes, the effect of increasing the size of the APC on

mixing is assessed. These results provide a better understanding of the VFPR as well as a

framework for the development of a dynamic immunoadsorption model for the device, which

is in described in Chapter 4.

3.2 METHODS

3.2.1 Reactor Prototypes

The small-scale prototype was identical to the one used in Chapter 2 and in the

previous heparinase I experiments conducted by Ameer and co-workers [1999]. The new,

larger VFPR prototype was constructed with a 22% longer and 90% thicker active

compartment (Figure 3.1). The compartmental volumes and pertinent length-scales of the

two VFPR prototypes are compared by Table 3.1 and Table 3.2, respectively.

* Some of the material in this chapter has been reprinted from Chemical Engineering Science, Vol. 56, No. 18, “Modeling the mixing behavior of a novel fluidized extracorporeal immunoadsorber,” E. A. Grovender, C. L. Cooney, G. A. Ameer, R. S. Langer, 5437-5441, Copyright 2001, with permission from Elsevier [Grovender et al., 2001] (http://www.sciencedirect.com/science/journal/00092509). Single copies of this chapter can be downloaded and printed only for the reader's personal research and study.

http://www.sciencedirect.com/science/journal/00092509

46

Prototype Blood Compartment Volume

[mL]

Active Plasma Compartment

[mL]

Plasma Collection Chamber

[mL]

Small 50 70 5

Large 60 175 10

Prototype Shaft Radius

[cm]

Membrane Radius

[cm]

Mesh Radius

[cm]

Membrane Length

[cm]

Mesh Length [cm]

Small 2.70 2.86 3.20 11 6.4

Large 2.70 2.86 3.49 14 6.4

3.2.2 Residence Time Distribution Experiments

The RTD experiments were conducted by injecting a pulse of dye into the VFPR

inlet, as depicted in Figure 3.2. The outlet dye concentration measurements were taken from

the blood and plasma ports during separate experiments and normalized to obtain the RTD

function, E(t). The injections of dye ranged from 0.5-2.0 mL, depending on the outlet port

and prototype considered. The dye was a 50 mg/mL aqueous solution of blue dextran (2,000

kD). The dye concentration measurements were made by reading the absorbance at 620 nm

in a flow-cell cuvette using a spectrophotometer capable of real-time data acquisition

(Shimatzu UV-1601). The tubing connecting the VFPR to the spectrophotometer was treated

as an ideal plug and was accounted for by subtracting the calculated residence time from the

RTD data.

In accordance with the β2m-immunoadsorption experiments presented in Chapter 2,

the main pump flowrate was set to 200 mL/min, the plasma pump flowrate was set to 50

ml/min, and the shaft rotation rate was set at 1.2x103 rpm. Additional RTD experiments

were conducted with the plasma pump set at 100 mL/min. To determine the effect of the

fluidized particles on the mixing of the device, experiments were conducted at both plasma

pump flowrates with and without of swollen polyacrylamide gel beads (90-180 µm diameter,

Bio-Rad No. 150-4140). This type of bead was selected because it effectively excludes blue

Table 3.1 Comparison of the compartmental volumes of the two VFPR Prototypes.

Table 3.2 Comparison of the pertinent length scales of the two VFPR Prototypes.

47

dextran from its pores. The same 69% suspended volume fraction of gel beads was used in

both prototypes (48 mL and 120 mL on a settled bed volume basis for the small and large

prototypes, respectively).

3.2.3 Mathematical Modeling

The macroscopic mixing behavior of each physical compartment within the VFPR is

described using the standard �tanks-in-series� model [Levenspiel, 1999]. This model

assumes that the real mixing pattern of a compartment can be described as a series of ideally

well-mixed control volumes, or CSTRs (constant stirred tank reactors). The residence times

of fluid exiting the blood and plasma ports, τbport and τpport, are calculated by integrating the

empirical RTD functions. The number of CSTRs in the blood compartment, NBC, is

determined by regressing the tanks-in-series analytical solution [Levenspiel, 1999] to the

RTD of the blood port, Ebport(t). A key assumption of the standard tanks-in-series model is

that the CSTRs have equal residence times. Typically in this model the volumetric flowrate

of fluid between CSTRs is constant, yielding a series of equal volume CSTRs. However, the

axial flowrate varies with axial position within the VFPR�s blood compartment, due to the

loss of flow across the microporous membrane. Therefore, each theoretical CSTR in the

blood compartment has a unique inlet flowrate, membrane surface area, and volume as

shown by Figure 3.3.

It then follows that the residence time of each CSTR in the blood compartment, τBC,i,

is described by Equation 3.1.

, 1,,

, , , 1

bport BC i iBC i

BC m i BC i BC i

V VN Q Q Qτ

τ−

= = =+

[3.1]

Here VBC,i is the volume, Qm,i is the transmembrane volumetric flowrate, and QBC,i is the non-

transmembrane outlet volumetric flowrate of an arbitrary blood compartment CSTR. The

flow across the microporous membrane is assumed to be uniformly distributed, which yields

Equation 3.2.

, ,m

m i BC iBC

QQ VV

=

[3.2]

Here Qm is the total transmembrane, or plasma pump flowrate, and VBC is the total volume of

the blood compartment, defined by Equation 3.3 (total conservation of volume within the

48

blood compartment). The non-transmembrane outlet volumetric flowrate of an arbitrary

blood compartment CSTR, QBC,i, is calculated by Equation 3.4 (incompressible flow).

,1

BCN

BC BC ii

V V=

=∑ [3.3]

, ,0 ,1

i

BC i BC m jj

Q Q Q=

= −∑ [3.4]

Here QBC,0 is the VFPR inlet volumetric flowrate. Equations 3.1, 3.2 and 3.4 are combined to

yield Equation 3.5,

, , ,0 , ,1

im

BC i BC i BC m i BC jjBC

QV Q Q VV

τ=

= + −

∑ [3.5]

Equations 3.3 and 3.5 are used to calculate the blood compartment CSTRs in an iterative

fashion.

The number of CSTRs in the active plasma compartment (APC), NAPC, is determined

by regressing Equations 3.6-3.12 to the empirical RTD of the plasma port, Epport(t).

( ),, 1 ,

,

1BC iBC i BC i

BC i

dCC C

dt τ −= − [3.6]

( ),, 1 ,

,

1APC iAPC i APC i

APC i

dCC C

dt τ −= − [3.7]

( ),1

APC

PCCAPC N PCC

PCC

dC C Cdt τ

= − [3.8]

Here CBC,i and CAPC,i are the dye concentrations of arbitrary blood and plasma compartment

CSTRs, respectively. CPCC is the dye concentration in the plasma collection chamber, which

is assumed to be one CSTR. Thus, CPCC is also the dye concentration exiting the plasma

port. τAPC,i is the residence time of an arbitrary plasma compartment CSTR, while τPCC is the

residence time of the plasma collection chamber. These residence times are defined by

Equations 3.9 and 3.10.

,

bulkAPC APC

APC iAPC APC m

VN N Qττ = = [3.9]

PCCPCC

m

VQ

τ = [3.10]

49

Here bulkAPCV and is the volume of the active plasma compartment minus the volume of the

bead spheres, while VPCC is the volume of the plasma collection chamber. τAPC is the

residence time of the entire APC (assuming that the dye is excluded from the gel bead pores).

The average dye concentration flowing across the microporous membrane, mC , and the mean

residence time of fluid flowing across the microporous membrane, τm, are defined by

Equations 3.11 and 3.12.

,0 , , , ,1 1

1 1( ) ( ) ( )BC BCN N

m APC m i BC i BC i BC ii im BC

C t C Q C t V C tQ V= =

= = = ∑ ∑ [3.11]

,,

1

BCNBC i

m BC iiBC

iVVτ

τ=

= ∑ [3.12]

The value for bulkAPCV is calculated from the specified values of VPCC and Qm and the

calculated values of τm and τpport. The initial conditions of the system of equations are: 1) the

first blood compartment CSTR contains a finite amount of dye and 2) the remaining

compartments contain no dye. The model differential equations were integrated numerically

using a fourth-order Runge-Kutta method.

3.3 RESULTS AND DISCUSSION

Analysis of RTD curves can be a powerful tool for characterizing the real mixing

patterns within a reaction vessel. Using methods similar to those described in this chapter,

two RTD data sets were previously obtained from the blood port of a prototype VFPR

(plasma line connections shown in Figure 1.2 and Figure 3.2) [Ameer et al., 1999]. These

separate data sets were used to gain preliminary insight into the mixing behavior of the APC

during steady-state enzymatic reactions. To mathematically simplify the VFPR model, the

APC, collection chamber, and plasma line were treated as one compartment. Furthermore,

the RTD of fluid exiting the blood compartment through the microporous membrane was

assumed to be identical to that exiting from the blood port. These assumptions were not

supported by the β2m-immunoadsorption data presented in Chapter 2. Therefore, the

development of a more rigorous compartmental model for the VFPR was deemed necessary.

In this chapter, experimental and modeling approaches are presented to better

understand the mixing pattern within the VFPR and to assess the effects of gel loading and

50

changes in design specifications on mixing. Figure 3.4 illustrates the mixing behavior of the

blood compartments of the two prototypes, while Table 3.3 and Table 3.4 list the model

parameters calculated from the blood port RTD data. By comparing the values of τbport and

NBC for the small prototype, it was concluded that the effect of loading gel beads into the

APC on the blood compartment�s mixing pattern is negligible. The same was assumed to be

true for the large prototype, as the only difference in its blood compartment specifications

was a 22% increase in membrane length.

Qm [mL/min]

Gel [mL]

ττττbport [s]

2bportr [-]

ττττm [s]

NBC [-]

VBC [mL]

50 0 14.6 0.9829 7.9 8 43

50 48 14.0 0.9912 7.6 8 41

100 0 19.0 0.9817 9.8 7 48

100 48 19.2 0.9786 9.9 7 48

Qm [mL/min]

Gel [mL]

ττττbport [s]

2bportr [-]

ττττm [s]

NBC [-]

VBC [mL]

50 0 17.8 0.9768 9.6 8 51

75 0 19.2 0.9784 10.4 8 52

100 0 21.1 0.9717 10.7 8 53

Figure 3.5 illustrates the mixing patterns of fluid exiting through the plasma ports of

the two prototypes, which were loaded with the same volume fraction of gel. Table 3.5 and

Table 3.6 list the model parameters calculated from the plasma port RTD data. For a given

prototype and flowrate, loading gel beads into the APC decreases the values of bulkAPCV and

τpport because the dye is excluded by the gel. According the model regression, the bulk fluid

volumes within the APC of each prototype essentially behave as single CSTRs (NAPC = 1, 2pportr > 0.98) at the 50 mL/min plasma pump flowrate, regardless of gel loading. Hence, it

Table 3.3 Model parameters calculated from the blood port RTD data for the small VFPR prototype.

Table 3.4 Model parameters calculated from the blood port RTD data for the large VFPR prototype.

51

was concluded that gel loading does not significantly affect macroscopic mixing at these

process conditions. At the 100 mL/min plasma pump flowrate, the bulk fluid volumes within

the APC of each prototype essentially behave as single CSTRs (NAPC = 1, 2pportr > 0.95),

provided that gel is not loaded. However, at the 100 mL/min plasma pump flowrate, it was

found that gel loading decreases mixing within the APC of each prototype (NAPC = 2, Figure

3.5, flow visualization). Therefore, it was concluded that the time-scale of mixing is

modulated by the presence of the gel suspension when the plasma pump flowrate is doubled.

The model is able to describe the plasma port RTD data from the large prototype better than

that obtained from the small prototype with gel loaded at the 100 mL/min plasma pump

flowrate ( 2pportr = 0.97 vs. 0.87, Figure 3.5). This suggests that the increase in the time-scale

of mixing, due to the increase in the radial thickness of the active compartment, is more than

offset by the associated increase in residence time (τAPC). Hence, the new VFPR prototype is

expected to provide additional effective capacity for active gel particles and membrane

surface area for increased plasma flowrates during blood detoxification. Meanwhile, the

large VFPR design only represents a small (10 mL) increase in the whole blood priming

volume.

Qm [mL/min]

Gel [mL]

ττττpport [s]

2pportr [-]

ττττAPC [s]

NAPC [-]

bulkAPCV

[mL]

50 0 108 0.9955 95 1 79

50 48 80 0.9966 66 1 55

100 0 59 0.9807 46 1 77

100 48 46 0.8671 33 2 55

Measuring the RTD at a plasma flowrate of 100 mL/min represents an extreme case

that may not be clinically feasible for these prototypes; nevertheless, the model describes this

condition moderately well. For instance, the β2m-immunoadsorption experiments were

performed with the small prototype at a plasma flowrate of 50 mL/min (Chapter 2) and the

plasma separation rate of the device that was used for those studies is limited to

approximately 60-70 mL/min. Assuming that the maximum hemofiltration rate is

Table 3.5 Model Parameters calculated from the plasma port RTD data for the small VFPR prototype.

52

proportional to the membrane surface area, the expected maximum plasma pump flowrate for

the large prototype is 73-85 mL/min.

Qm [mL/min]

Gel [mL]

ττττpport [s]

2pportr [-]

ττττAPC [s]

NAPC [-]

bulkAPCV

[mL]

50 0 226 0.9989 205 1 170

50 120 143 0.9860 122 1 102

75 0 158 0.9761 140 1 175

75 120 103 0.9410 84 1 106

100 0 124 0.9596 107 1 178

100 120 78 0.9711 62 2 103

In summary, RTD data sets were collected from the plasma and blood ports

separately for the studies presented in this chapter. The new model treats each physical

compartment within the VFPR individually. It also accounts for, at least partially, the

differences in RTD of the fluid exiting the blood compartment through the blood port and the

microporous membrane. The model regression revealed that the bulk fluid within the APC

was well-mixed (NAPC = 1) at a plasma pump flowrate of 50 ml/min, with or without gel

beads. The results of this study will be incorporated into a dynamic adsorption model for the

VFPR (Chapter 4).

Table 3.6 Model Parameters calculated from the plasma port RTD data for the large VFPR prototype.

53

Figure 3.1 Photograph of the new, larger VFPR prototype. The device is partially disassembled for display purposes. The compartment volumes and pertinent length scales are provided in Table 3.1 and Table 3.2.

PlasmaLine Ports

RotatingInner Shaft

Inlet Port

Bottom Cap

Top CapOutlet Port

Membrane

Mesh

54

Figure 3.2 Schematic diagram of the experimental setup used to obtain RTDs from the plasma port. The spectrophotometer was moved to the blood port to obtain the RTDs of the blood compartment (not shown).

Figure 3.3 The compartmental mixing model for the VFPR.

PlasmaPort

CollectionChamber

+++

Membrane

m

m

CQ

,1

bulkAPC

APC

APC

VNC , APC

bulkAPC

APC

APC N

VN

C

,PCC PCCV C

Mesh

PlasmaChamber

InletPort

, BCBC NQ

, BCm NQ

, 1BCBC NQ −

BloodPort

,

,

BC

BC

BC N

BC N

V

C

,2

,2

BC

BC

VC

,1

,1

BC

BC

VC

,2BCQ

,1BCQ

2,mQ

1,mQ

Blood Chamber

,0 ,0,BC BCQ C

VFPR

WaterSupply

Main Pump

Port PlugBloodPort

Plasma Port

PlasmaPump

Spectro-photometer

Dye Injection

55

Figure 3.4 Blood port residence time distribution functions for the small (top: a,b) and large (bottom: c,d) VFPR prototypes at plasma pump flowrates of 50 (left: a,c) and 100 (right: b,d) mL/min. The average data sets (N=3, SEM < 0.0025 s-1) and model curves are shown for the experiments conducted without gel loaded into the active plasma compartment.

(a)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 10 20 30 40 50Time, sec

Ebp

ort(t

) , 1

/sec

Data

Model

(b)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 10 20 30 40 50Time, sec

Ebp

ort(t

) , 1

/sec

(d)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 10 20 30 40 50Time, sec

Ebp

ort(t

) , 1

/sec

(c)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 10 20 30 40 50Time, sec

Ebp

ort(t

) , 1

/sec

56

Figure 3.5 Plasma port RTD curves for the small (top: a,b) and large (bottom: c,d) VFPR prototypes at plasma pump flowrates of 50 (left: a,c) and 100 (right: b,d) mL/min. The average data sets (N=3, SEM < 0.0005 s-1) and model curves are shown for the experiments conducted with gel loaded into the active plasma compartment.

(a)

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0 100 200 300 400 500 600Time, sec

Epp

ort(t

) , 1

/sec

Data

Model

(b)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 100 200 300 400 500 600Time, sec

Epp

ort(t

) , 1

/sec

(d)

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0 100 200 300 400 500 600Time, sec

Epp

ort(t

) , 1

/sec

(c)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 100 200 300 400 500 600Time, sec

Epp

ort(t

) , 1

/sec

57

3.4 REFERENCES Ameer GA, EA Grovender, B Obradovic, CL Cooney and R Langer (1999) "Rtd Analysis of a Novel Taylor-Couette Flow Device for Blood Detoxification." AIChE Journal. 45: 633-8.

Grovender EA, CL Cooney, RS Langer and GA Ameer (2001) "Modeling the Mixing Behavior of a Novel Fluidized Extracorporeal Immunoadsorber." Chem Eng Sci. 56: 5437-41.

Levenspiel O (1999) Chemical Reaction Engineering, John Wiley and Sons, New York.

59

Chapter 4: Immunoadsorption Model for the VFPR* 4.1 INTRODUCTION

From an engineering perspective, it would be useful to have a dynamic

immunoadsorption model for the VFPR to aid in the design of device prototypes, in vitro

experiments, and potential clinical trials. To derive such a model, the mass-transfer and

adsorption processes within the VFPR need to be described. Towards this end, experimental

and mathematical methods for characterizing the macroscopic mixing pattern within an

immunoadsorptive VFPR were described in Chapter 3. In this chapter, the equilibrium

behavior of immunoadsorptive gel beads is characterized using the Langmuir adsorption

isotherm and confocal microscopy. Furthermore, the importance of external mass-transfer

resistances within the active plasma compartment (APC) is assessed through dissolution

studies conducted with benzoic acid particles. These results are used to develop a dynamic

immunoadsorption model that describes the performance of the immunoadsorptive VFPR

without using any adjustable parameters.

4.2 IMMUNOADSORPTIVE GEL

Thus far, the immunoadsorptive media used with VFPR devices has consisted of anti-

β2m monoclonal antibodies immobilized onto 4% agarose gel beads (Chapter 2). In this

section, the partitioning, diffusion, and adsorption of β2m within the immunoadsorptive gel

beads is described. These characteristics of the immunoadsorbent are used later in the

derivation and solution of the dynamic immunoadsorption model equations for the VFPR.

4.2.1 Solute Partitioning

The partition coefficient of β2m in the gel (Φ) is defined on a total bead volume basis

by Equation 4.1. The value of this parameter is estimated using Equation 4.2, a relation

derived by Ogston [1958] for dilute solutions of uncharged, spherical macromolecules in an

array of randomly arranged cylindrical fibers.

* This chapter is a revised version of a research article originally published in the AIChE Journal [Grovender et al., 2002]. It has been reproduced with permission of the American Institute of Chemical Engineers. Copyright © 2002 AIChE. All rights reserved.

60

gel

bulk

CC

Φ ≡ [4.1]

2

exp 1 s

f

rr

φ Φ = − +

[4.2]

Here Cbulk is the concentration of desorbed β2m in the bulk fluid, Cgel is the concentration of

desorbed β2m inside the beads on a total gel volume basis, and φ is the volume fraction of

polymer fibers within the gel beads (φ = 0.04). The average radius of the agarose fibers, rf, is

taken to be 1.9x10-9 m, which was the value measured by Djabourov and co-workers [1989]

using small-angle X-ray scattering. The hydrated radius of β2m, rs, was estimated to be

1.7x10-9 m by assuming that β2m has the specific volume and degree of hydration of a typical

globular protein [Cantor and Schimmel, 1980].

4.2.2 Adsorption Isotherm

The antigen-antibody equilibrium dissociation constant, KD, is defined by Equation

4.3, while an adsorption site mass-balance is given by Equation 4.4. The combination of

Equations 4.1, 4.3, and 4.4 results in the Langmuir adsorption isotherm, Equation 4.5.

2

eq eqs gel

D eqm

CK

β

ρρ

≡ [4.3]

2

0 eq eqs s mβρ ρ ρ= + [4.4]

2

00 eqeqs geleq s bulk

m eqeqD D gelbulk

CCK K CC

β

ρρρ = =++

Φ

[4.5]

On a total gel volume basis ρs and 2mβρ are the densities of adsorption sites and adsorbed

β2m, respectively. This is in contrast to the to the settled-bed volume basis that was used to

define ρ′s for Equation 2.1. The superscripts 0 and eq refer to the initial and equilibrium

values, respectively.

A β2m mass-balance (Equation 4.6) can be used with Equations 4.1 and 4.5 to obtain

Equation 4.7, a form of the Langmuir adsorption isotherm in terms of measurable variables.

[ ] [ ]2

0 0(1 ) (1 ) (1 )eq eq eqbed m total bed bulk bulk bed gel gelV V V C C V C Cβε ρ ε ε − = − − − + − − [4.6]

61

( )0

0(1 )(1 ) (1 ) eqeqtotal bed s bulk

bulk bulkeqDbedbulk

V V CC C KV C

ε ε ρ − − − Φ −− = +

Φ

[4.7]

Here Vtotal is the total volume of the system, Vbed is the settled-bed volume of

immunoadsorbent, and ε is the settled-bed void fraction. For cases when Φ~1 or Vbed <<

Vtotal, the left hand side of Equation 4.7 can be approximated as in Equation 4.8.

( ) ( )0 0(1 )(1 ) eq eqtotal bed totalbulk bulk bulk bulk

bed bed

V V VC C C CV V

ε − − − Φ − ≈ −

[4.8]

For the values of the parameters considered herein, this approximation represents an error of

less than 2%. The adsorption site density ( 0sρ ) of the immunoadsorptive gel was determined

in Chapter 2 by equilibrating samples with saturating amounts of β2m (where ρ′s = [1-ε] 0sρ ).

The same protocol and batch of immunoadsorbent was used with three sub-saturating

quantities of β2m to produce additional data, from which the value of KD was regressed by

minimizing SSE (Sum Squared Error).

4.2.3 Adsorption Site Distribution

Confocal microscopy* was used to assess the spatial distribution of β2m-adsorption

sites within the immunoadsorbent gel beads. Recombinant human β2m was prepared using

the protocol described in Chapter 2 and labeled with fluorescein-5-EX succinimidyl ester,

according to the instructions provided by the manufacturer (Molecular Probes, Eugene, OR).

Fluorescein-β2m (6 mg) was equilibrated with a sample of the immunoadsorptive gel (0.20

mL) in phosphate buffered saline (pH 7.4; PBS). The sample was combined with an equal

volume of anti-bleaching buffer (10 µg p-phenylene diamine, 1.5 mL deionized water, and 1

mL 10x PBS brought to a total volume of 10 mL with glycerol) and studied with a Zeiss

LSM 510 confocal microscope (Oberkochen, Germany). Two additional samples were

analyzed as controls: 1) gel beads without immobilized antibody, but equilibrated with

fluorescein-β2m and 2) gel beads with immobilized antibody, but not equilibrated with

fluorescein-β2m.

* This work was conducted utilizing the W. M. Keck Foundation Biological Imaging Facility at the Whitehead Institute.

62

4.2.4 Effective Diffusivity

The effective diffusivity (De) of β2m inside the gel beads was calculated using

Equation 4.9, where Dw is the diffusion coefficient of β2m in dilute aqueous solution and θ is

the diffusion hindrance exerted by the gel polymer fibers.

e wD Dθ= [4.9]

The value of Dw was estimated at 37OC (1.8x10-10 m2/s) using a correlation for large

molecules including proteins [Polson, 1950] and θ was assumed to be the measured value

(0.63) reported by Johnson and co-workers [1996] for lactalbumin (a 1.4x104 g/mol globular

protein) in 4% agarose gel.

4.3 DEVICE MODEL

4.3.1 Blood Compartment

Figure 4.1 illustrates the dynamic adsorption model for the VFPR. Through residence

time distribution studies and mathematical modeling it was shown in Chapter 3 that the

macroscopic mixing behavior within the blood compartment can be well represented by a

series of NBC ideally well-mixed tanks. The residence time (τBC,i) of blood plasma in each

tank is constant, but each tank has its own unique volume (VBC,i). Equations 4.10-4.14

represent a mass balance of β2m within the blood compartment, taking into account

hemofiltration into the APC.

( ),, 1 ,

,

1BC iBC i BC i

BC i

dCC C

dt τ −= − [4.10]

, ,,

, , ,

(1 )(1 )

BC i BC iBC i

m i BC i BC i

H VQ Q H

τ−

=+ −

[4.11]

,0 ,0,

,0 ,1

BC BCBC i i

BC m ij

Q HH

Q Q=

=−∑

[4.12]

, ,m

m i BC iBC

QQ VV

=

[4.13]

, , 1 ,BC i BC i m iQ Q Q−= − [4.14]

63

Here CBC,0 , HBC,0 and QBC,0 are the inlet plasma β2m concentration, hematocrit (volume

fraction of blood cells), and whole blood volumetric flowrate, respectively. The plasma

pump controls the total volumetric flowrate of plasma across the microporous membrane into

the active compartment, Qm. For the ith tank-in-series, CBC,i is the plasma concentration of

β2m, HBC,i is the hematocrit, QBC,i is the outlet volumetric flowrate of whole blood, and Qm,i is

the volumetric flowrate of plasma across the membrane. The total volume of the blood

compartment is VBC. The β2m concentration of plasma crossing the membrane, mC , is given

by Equation 4.15.

( ), ,1

1 BCN

m BC i BC iiBC

C V CV =

= ∑ [4.15]

4.3.2 Active Plasma Compartment (APC)

The APC houses the immunoadsorptive media, which consists of an antibody

immobilized onto porous agarose gel beads. The model for the APC incorporates the

following assumptions: 1) the intrinsic antibody-antigen association rate is instantaneous, 2)

the adsorption sites are uniformly distributed inside the gel beads, 3) the adsorption

equilibrium follows the Langmuir isotherm, 4) the bulk fluid within the APC behaves as a

single well-mixed control volume (Chapter 3), and 5) the size of the gel beads can be well

represented by the volume-average radius, R.

Equation 4.16 represents a mass balance for β2m in the bulk fluid of the APC. The

first term on the right-hand side of Equation 4.16 accounts for convective flow through the

APC; the second term accounts for transport of β2m to the surface of the active beads.

( ) ( ) ( )1 surfaceAPCAPC bed m m APC surface m APC APC

dCV V Q C C A k C Cdt

ε− − = − + − [4.16]

Here VAPC is the total volume of the APC and mk is the mass-transfer coefficient for the

transport of β2m from the bulk fluid to the surface of the gel beads. The β2m concentrations

within the bulk fluid and at the outer surface of the gel beads are CAPC and surfaceAPCC ,

respectively. The total surface area of the gel, Asurface, is expressed by Equation 4.17 in terms

of previously defined parameters, where Nbeads is the total number of gel beads in the APC.

64

( ) ( )2 23

(1 ) 3(1 )4 4(4 3)

bed bedsurface beads

V VA N R RR Rε επ π

π − −= = =

[4.17]

Equations 4.1, 4.16, and 4.17 are combined to yield Equation 4.18 which, along with

Equations 4.19 and 4.20, are used to model dynamics of the β2m concentration of the bulk

fluid within the APC.

( ) [ ]3 (1 )1

(1 )

surfacegelAPC bed

m APC APCAPC EMT APC bed

CdC VC C Cdt V V

ετ τ ε

−= − + − − − Φ [4.18]

(1 )APC bedAPC

m

V VQ

ετ − −= [4.19]

EMTm

Rk

τ = [4.20]

Here the characteristic time-scale of external mass-transfer (or the transport of β2m to the

surface of the active beads) is τEMT and τAPC is the residence time of the bulk fluid volume.

Using the aforementioned assumptions, the species conservation equation for

desorbed β2m within an immunoadsorptive gel bead is reduced to the form shown by

Equation 4.21. The rate of adsorption, Radsorption, is expressed in the convenient form shown

by Equation 4.22.

22

1gel gele adsorption

C CD r R

t r r r∂ ∂ ∂= − ∂ ∂ ∂

[4.21]

2m geladsorption

gel

CR

C tβρ∂ ∂

= ∂ ∂ [4.22]

The Langmuir adsorption isotherm, or Equation 4.5, is combined with Equations 4.21

and 4.22 to yield Equations 4.23 and 4.24 which represent a mass balance for β2m within a

gel bead. Here the characteristic time-scale of internal mass-transfer within the porous beads

is τIMT . Equation 4.23 has previously been derived and used to model the adsorption of

albumin onto ion exchange resin [Leaver et al., 1992]. Equations 4.25 and 4.26 represent the

boundary conditions that were used to solve Equation 4.23, where the superscripts surface and center refer to their respective radial postions.

65

( )

1202

2 2

21gel gel gelS D

IMT D gel

C C CKRt r r rK C

ρτ

− ∂ ∂ ∂ = + + ∂ ∂ ∂+

[4.23]

2

IMTe

RD

τ = [4.24]

surfacesurface

gel gelm APC e

C Ck C D

r ∂

− = Φ ∂ [4.25]

0center

gelCr

∂ = ∂

[4.26]

4.3.3 Plasma Line, Collection Chamber, and Blood Outlet Port

The plasma line and collection chamber are lumped together as a single well-mixed

control volume and modeled by Equations 4.27-4.28. Here CPLCC , VPLCC, and τPLCC are the

lumped β2m concentration, volume, and residence time, respectively. The plasma β2m

concentration of partially cleansed whole blood exiting the VFPR, CVFPR, is calculated by

Equation 4.29.

( )1PLCCAPC PLCC

PLCC

dC C Cdt τ

= − [4.27]

PLCCPLCC

m

VQ

τ = [4.28]

,0 , ,

,0 ,0

( )(1 )(1 )

BC BCm PLCC BC m BC N BC NVFPR

BC BC

Q C Q Q H CC

Q H+ − −

=−

[4.29]

4.4 RESERVOIR MODEL

The VFPR is usually connected to a β2m reservoir in a closed-loop circuit for blood

detoxification (Figure 4.2). This reservoir can be comprised of a bag of donated blood, an

animal model, or a human patient. To date, β2m-immunoadsorption experiments with the

VFPR have been limited to bags of whole human blood (Chapter 2). Equations 4.30 and

4.31 represent the mass balance of β2m in a blood bag (530 mL) and its circuit tubing (65

66

mL). These two volumes are lumped together as VBR. Equations 4.32 and 4.33

mathematically connect the reservoir to the VFPR device in a closed-loop circuit.

( ),, 1 ,

,

1BR iBR i BR i

BR i

dCC C

dt τ −= − [4.30]

,BR BR

BR iBR BR BR

VN N Qττ = = [4.31]

,0BR VFPRC C= [4.32]

,0 , BRBC BR NC C= [4.33]

Here NBR is the number of theoretical tanks representing VBR. For the ith tank-in-series, CBR,i

is the plasma β2m concentration and τBR,i is the residence time.

4.5 CHARACTERIZATION OF MASS-TRANSFER TO THE SURFACE OF SUSPENDED PARTICLES The importance of mass-transfer resistance at the external surface of the suspended

gel beads (τEMT, Equation 4.20) relative to the mass-transfer resistance associated with the

hemofiltration rate (τAPC, Equation 4.19) was assessed through dissolution studies conducted

with small, non-spherical particles of benzoic acid. These particles were created using a

method similar to one previously described by Moore [1994]. Briefly, benzoic acid was

melted, solidified into a flat sheet on aluminum foil, and crushed with a ceramic mortar and

pestle. Irregularly shaped particles approximately 100 µm in size were obtained by sifting

the crushed benzoic acid between 150 µm and 75 µm nominal opening stainless steel sieves

(VWR, Westchester, PA).

The dissolution studies were conducted as shown in Figure 4.3. The active plasma

compartment was flushed for 5 minutes (>3.5 residence times) to remove most (>95%) of the

dissolved benzoic acid that was injected along with the solid particles. During the following

5 minute experimental period, samples were taken every 60 seconds and immediately filtered

to remove any remaining fine particles (0.45 µm Millipore catalog number SLHV R04 NL,

Bedford, MA). The concentration of benzoic acid was measured by reading the absorbance

at 250 nm (diluting the samples as necessary with 0.01% Triton X-100).

67

4.6 COMPUTATIONAL METHODS

Equations 4.10-4.15, 4.18-4.20, and 4.23-4.33 model the dynamics of β2m adsorption

within the VFPR and the subsequent removal of β2m from a blood reservoir. The Forward-

Time Centered-Space (FTCS) method was used to convert Equation 4.23 into a discrete form

(200 finite radial sections) and the second-order Runge-Kutta algorithm was applied to

integrate the differential equations [Press et al., 1992]. Input parameters (including initial

conditions, with superscripts t=0) used for the model calculations are listed in Table 1. At

each time-step, the total mass-balance error for Equations 4.10-4.15, 4.18-4.20, and 4.23-4.33

was kept below 0.5%. A copy of the FORTRAN program used to perform the model

calculations is provided in the Appendix.

4.7 RESULTS AND DISCUSSION

The VFPR is a multi-compartment Taylor-Couette flow hemofilter designed to

remove toxins from a patient�s blood stream via heterogeneous adsorption or reaction. The

first immunoadsorption application has been the removal of the amyloid-associated protein

β2-microglobulin from human blood in vitro. This technology, we believe, can be used for

understanding and treating the progression of Dialysis-Related Amyloidosis, a devastating

complication of long-term kidney failure, by targeting a specific macromolecule and

monitoring the effect of its removal on the patient via clinical trials. To lay a solid

foundation for the derivation of a dynamic model, the equilibrium behavior of the

immunoadsorbent and the mass-transfer characteristics of the VFPR were investigated

independently.

Over the β2m concentration range considered, the Langmuir isotherm describes

equilibrium β2m adsorption data (Figure 4.4). The value of the antibody-antigen dissociation

constant (KD = 0.1 ± 0.1 mg/L) is significantly smaller than the lower limit of the β2m

concentration range (1.0 - 3.0 mg/L) in the circulation of healthy individuals [Floege and

Ketteler, 2001]. Therefore, this model immunoadsorbent appears to have sufficient affinity

for therapeutic application.

The cross-sectional confocal micrograph of a typical immunoadsorptive gel bead

shows that the β2m adsorption sites are uniformly distributed throughout the polymer

(Figure 4.5a). This was a key assumption in the numerical solution of Equation 4.23 (i.e.

68

0sρ is not a function of radial position). Meanwhile, the defect in the atypical bead

demonstrates the ability of the imaging technique to detect regions inside the gel that lack

adsorbed β2m (Figure 4.5b). These results demonstrate the utility of confocal microscopy for

the characterization of porous matrices.

During the dissolution studies the observed concentration of benzoic acid (3.0±0.1

g/L) exiting the VFPR through the plasma line did not significantly differ from the solubility

limit (2.9 g/L at 20oC) [Budavari et al., 1989]. This strongly suggests that external mass-

transfer resistances within the active plasma compartment are not rate limiting under the

process conditions considered. In order to provide flexibility for other process conditions

that may arise in the future, the derivation of the VFPR model accounts for the possibility of

a rate-limiting external mass-transfer resistance through the mass-transfer coefficient, mk . In

accordance with the findings of the dissolution studies, mk was assigned a finite value

sufficiently large such that τEMT << τIMT and τEMT << τAPC (Table 4.1 and Equations 4.19,

4.20, and 4.24). Thus, external mass-transfer resistance did not have any appreciable effect

on the immunoadsorption dynamics calculated by the model for the experiment considered

(refer to the sensitivity analysis below and Figure 4.7a). However, the second term on the

right-hand side of Equation 4.18 is required in any case to account for the transport of β2m to

the surface of the gel beads.

The model�s ability to describe VFPR performance was tested with a set of input

parameters corresponding to a previously conducted β2m-adsorption experiment (Table 4.1).

Without adjusting any of the parameters, the dynamic immunoadsorption model is able to

describe the performance of the VFPR (Figure 4.6, Equations 4.10-4.15, 4.18-4.20 and 4.23-

4.33). It is important to note that the equilibrium concentration of β2m is on the order of the

antibody-antigen dissociation constant (KD). This is the case because the system was

charged, approximately, with a 1:1 stoichiometric ratio of β2m and adsorption sites. Under

clinical operating conditions, an immunoadsorptive VFPR would likely contain an excess

number of adsorption sites. In separate β2m immunoadsorption experiments that were

conducted with excess adsorption sites, the equilibrium β2m concentrations were below

detectable limits (Chapter 2).

69

Parameter Value Units Parameter Value Units

0tAPCC = 0 mg/L Qm 50* mL/min

0,

tBC iC = 3.2* mg/L R 46�

0,

tBR iC = 3.2* mg/L VBC 46.5§,�� mL

0tgelC = 0 mg/L VBC,i 6.6, 6.3, 6.1, 5.9 mL

0tPLCCC = 0 mg/L 5.7, 5.5, 5.3, 5.1§,��

De 1.1 x10-10 m2/s VAPC 79§ mL

HBR 0.31� - Vbed 48* mL

KD 0.1 mg/L VBR 595* mL

mk 10-3 m/s VPLCC 15* mL

NBC 8§,�� - ε 0.4** -

NBR 3§,�� - Φ 0.87 -

QBR 200* mL/min 0sρ 50*,�� mg/L

A sensitivity analysis was conducted on the external mass-transfer coefficient ( mk ) to

confirm that increasing the value of mk above the arbitrarily assigned value does not have a

significant effect on the model predictions (Figure 4.7a). Furthermore, the model�s

flexibility to account for external mass-transfer resistances is demonstrated by the shape of

the plasma line model curve for the low value of mk (τEMT ∼ τIMT). The assumption that the

population of gel beads can be well represented by the volume-average radius was tested by a

sensitivity analysis on R (Figure 4.7b). Varying the value of this parameter by one standard

of deviation has an effect on the shape of the plasma line concentration curve; however, this

* Chapter 2 [Ameer et al., 2001] � Data provided by the manufacturer. � After accounting for dilution by the priming saline. § Chapter 3 [Grovender et al., 2001] ** Calculated from the total and void volumes measured in a packed column (acetone and pore-excluded aggregate protein markers; Bio-Rad #151-1901, Hercules, CA). �� The mixing behavior was re-characterized through similar RTD studies using a 36% glycerol-in-water solution at 20OC to better account for the viscosity and density of whole blood [Wolf et al., 1984; Fournier, 1999]. �� Value previously reported on a settled-bed volume basis.

Table 4.1 Model input parameters.

70

effect is reasonably symmetric. Therefore, the assumption appears to be justified. Because

their values were estimated from the literature, sensitivity analyses on the hindered effective

diffusivity (De) and the solute partition coefficient (Φ) were performed (Figure 4.7c-Figure

4.7d). The variations considered (refer to Figure 4.7 caption) in De and Φ resulted in changes

of less than 15% in the calculated values of CPLCC at all time-points.

The dynamic immunoadsorption model for the VFPR was developed to facilitate the

development of the device and the optimization of its potential therapeutic application. With

the desire for a model capable of describing the VFPR�s performance over a range of

conditions, the model was based on fundamental transport theory and guided by the

independent characterization of the fluid dynamics and adsorption equilibrium. The model

calculations predict that the mass-transfer processes within the active compartment of the

VFPR do not control the rate of β2m-adsorption (Figure 4.7). Hence, we conclude that the

process controlling the β2m-adsorption rate within the VFPR is the hemofiltration rate (Qm =

50 mL/min), which is on the order of the reported flowrate of extravascular β2m into the

blood stream (approximately 70 mL/min) [Floege et al., 1991]. These two processes are

expected to be rate-controlling for β2m removal from a patient with the immunoadsorbent

VFPR. A major goal for the future development of the VFPR will be to increase the

hemofiltration rate while maintaining the fast mass-transfer rates within the active plasma

compartment. The methods for characterizing the VFPR and the dynamic immunoadsorption

model presented herein should prove useful in this endeavor.

71

Figure 4.1 Schematic diagram of the dynamic VFPR adsorption model. The macroscopic mixing behavior of the blood compartment is described by a finite series of ideally well-mixed control volumes or �tanks.� The bulk fluid of the active plasma chamber and the lumped volume of the plasma line tubing & plasma collection chamber are each represented by a single tank.

Plasma LineTubing &CollectionChamber

(Equations 4.27-4.28)

+++

Membrane(Equation 4.15)

m

m

CQ

,

,APC APC

e m

V CD k

PLCC

PLCC

VC

Active PlasmaCompartment(Equations 4.18-

4.20, & 4.23-4.26)

, BCBC NQ

, BCm NQ

, 1BCBC NQ −

,

,

,

BC

BC

BC

BC N

BC N

BC N

V

CH

,2

,2

,2

BC

BC

BC

VCH

,1

,1

,1

BC

BC

BC

VCH

,2BCQ

,1BCQ

2,mQ

1,mQ

BloodCompartment

(Equations4.10-4.14)

+ +

Mesh

VFPRC

,0 ,0,BC BCQ CBlood Inlet(Equation 4.33)

Blood Outlet(Equation 4.29)

72

Figure 4.2 Closed-loop blood detoxification with the VFPR. The β2m reservoir represents either a human patient or a substituted model (i.e. a bag of blood) and the circuit tubing. The equations shown are provided as a convenience to the reader and are described throughout the text.

( )

( )

1202

2 2

2

(1 )

21

0

1

APC bedAPC

m

EMTm

gel gel gelS D

IMT D gel

IMTe

surfacesurfacegel gel

m APC e

centergel

PLCCAPC PLCC

PLCC

V VQ

Rk

C C CKRt r r rK C

RD

C Ck C D

r

Cr

dC C Cdt

ετ

τ

ρτ

τ

τ

−

− −=

=

∂ ∂ ∂ = + + ∂ ∂ ∂+

=

∂ − = Φ ∂

∂ = ∂

= −

,0 , ,

,0 ,0

( )(1 )(1 )

BC BC

PLCCPLCC

m

m PLCC BC m BC N BC NVFPR

BC BC

VQ

Q C Q Q H CC

Q H

τ =

+ − −=

−

( )

( )

( )

,, 1 ,

,

, ,,

, , ,

,0 ,0,

,0 ,1

, ,

, , 1 ,

, ,1

1

(1 )(1 )

1

1

BC

BC iBC i BC i

BC i

BC i BC iBC i

m i BC i BC i

BC BCBC i i

BC m ij

mm i BC i

BC

BC i BC i m i

N

m BC i BC iiBC

APCm APC

APC

dCC C

dtH V

Q Q HQ H

HQ Q

QQ VV

Q Q Q

C V CV

dC C Cdt

τ

τ

τ

−

=

−

=

= −

−=

+ −

=−

=

= −

=

= −

∑

∑

( ),, 1 ,

,

,

,0

,0 ,

1

BR

BR iBR i BR i

BR i

BR BRBR i

BR BR BR

BR VFPR

BC BR N

dCC C

dtV

N N QC CC C

τττ

−= −

= =

==

BloodCirculation

Pump

VFPREquations 4.10-4.15,

4.18-4.20, & 4.23-4.29

[ ]3 (1 )

(1 )

surfacegelbed

APCEMT APC bed

CV CV V

ετ ε

−+ − − − Φ

β2m ReservoirEquations 4.30-4.33

73

Figure 4.3 Apparatus used to conduct the dissolution studies. Agarose gel beads (40 mL Sepharose® CL-4B) were included in the active compartment in an attempt to duplicate the conditions of the dynamic β2m-adsorption experiments. The main pump flowrate (200 mL/min), plasma pump flowrate (50 mL/min), and cylinder rotation rate (1.2 x103 rpm) also matched those used during the β2m-adsorption experiments. Aggregation of the benzoic acid particles was prevented by adding 0.01% Triton X-100 to the system. It has previously been reported that the use of a similar non-ionic surfactant during benzoic acid dissolution studies has a minimal effect (<5%) on the mass-transfer rate [Gondoh et al., 1968].

VFPR

0.01%TritonX-100

Main Pump

PlugPlasma LineActive

Compartmentwith 9.8 g

Benzoic AcidParticles

Sample Collection

74

Figure 4.4 Equilibrium adsorption behavior of the immunoadsorptive media. Equations 4.7 and 4.8 were regressed to the saturated (Chapter 2) and sub-saturated data to determine the value of KD (0.1 ± 0.1 mg-β2m /L ~ 10 nmol-β2m /L). The value of ρs

0 (50 ± 3 mg-β2m/L-gel) was calculated from the saturated data (reported as ρ′s = 30 ± 2 mg-β2m/L-settled-bed in Chapter 2). The controls did not show significant fluorescence. Error bars and confidence intervals represent the standard error of the mean (SEM).

0

10

20

30

40

50

60

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Saturated Data

Sub-Saturated Data

Model

eqbulkC , mg/L

ρρ ρρ ββ ββ2m

, mg/

L x

eq

75

Figure 4.5 Confocal micrograph of the immunoadsorptive gel: center cross-section of a typical bead (a) and an atypical bead (b). β2m is shown in green. The controls showed no apparent adsorption of β2m or intrinsic fluorescence of the immunoadsorbent. The thickness of the cross-section shown is 0.40 µm and the resolution is 0.22 µm.

76

Figure 4.6 The predicted and observed dynamics of ββββ2m clearance from whole blood by an immunoadsorptive VFPR, in vitro. The model equations listed in Figure 4.2 and the input parameters listed in Table 2.1 were used to calculate the blood reservoir outlet and plasma line β2m concentrations. The blood reservoir outlet and plasma line data was first presented in Chapter 2. Error bars represent the standard error of the mean (SEM).

0.0

1.0

2.0

3.0

4.0

0 5 10 15 20 25 30 35 40 45Time, minutes

Blood Reservoir Data

Blood Reservoir Model

Plasma Line Data

Plasma Line Model

CBR

,NB

R o

r CPL

CC , m

g/L

77

Figure 4.7 Sensitivity analysis results for the model parameters mk (a), R (b), De (c),

and ΦΦΦΦ (d). The plasma line data (∆) was taken from Chapter 2 [Ameer et al., 2001] and

the error bars represent the standard error of the mean (SEM). The center values for the

model parameters are listed in Table 4.1. The high and low values are as follows: mk = 10-

2 & 10-5 m/s, R = 58 & 34 µm(±σ ), De = 1.8x10-10 & 0.7x10-10 m2/s (±20%), Φ = 1.00 &

0.75 (the measured value reported Johnson and co-workers [1995] for lactalbumin in 6%

agarose gel).

(a)

0.0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25 30

Time, minutes

DataCenterLowHigh

CPL

CC ,

mg/

L

(b)

0.0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25 30

Time, minutes

CPL

CC ,

mg/

L

(c)

0.0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25 30

Time, minutes

C PLCC

, m

g/L

(d)

0.0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25 30

Time, minutes

C PLCC

, m

g/L

78

4.8 REFERENCES Ameer GA, EA Grovender, H Ploegh, D Ting, WF Owen, M Rupnick and R Langer (2001) "A Novel Immunoadsorption Device for Removing Beta2-Microglobulin from Whole Blood." Kidney Int. 59: 1544-50.

Budavari S, MJ O'Neil, A Smith and PE Heckelman (1989) Merck & Company, Rahway, NJ: pp. 170.

Cantor CR and PR Schimmel (1980) Biophysical Chemistry: Techniques for the Study of Biological Structure and Function., W. H. Freeman and Company, New York.

Djabourov M, AH A. H. Clark, DW Rowlands and SB Ross-Murphy (1989) "Small-Angle X-Ray Scattering Characterization of Agarose Sols and Gels." Macromol Rev. 22: 180.



Fournier RL (1999) Taylor & Francis, Philadelphia: pp. 65.

Gondoh S, M Shiozawa, K Kusunoki and I Nakamori (1968) "Effects of Surfactants on the Solution Rate of Single Benzoic Acid Spheres in Water." Kagaku Kogaku. 32: 919.


Grovender EA, CL Cooney, RS Langer and GA Ameer (2001) "Modeling the Mixing Behavior of a Novel Fluidized Extracorporeal Immunoadsorber." Chem Eng Sci. 56: 5437-41.

Johnson EM, DA Berk, RK Jain and WM Deen (1995) "Diffusion and Partitioning of Proteins in Charged Agarose Gels." Biophysical Journal. 68: 1561-8.

Johnson EM, DA Berk, RK Jain and WM Deen (1996) "Hindered Diffusion in Agarose Gels: Test of Effective Medium Model." Biophysical Journal. 70: 1017-23.

Leaver G, JA Howell and JR Conder (1992) "Adsorption Kinetics of Albumin on a Cross-Linked Cellulose Chromatographic Ion Exchanger." J Chromatog. 509: 101.

Moore CMV (1994) Characterization of a Taylor-Couette Flow Reactor. Massachusetts Institute of Technology, Chemical Engineering: Cambridge.

Ogston AG (1958) "The Spaces in a Uniform Random Suspension of Fibers." Trans Faraday Soc. 54: 1754.

Polson A (1950) "Some Aspects of Diffusion in Solution and a Definition of a Colloid Particle." J Phys Colloid Chem. 54: 649.

Press WH, S. A. , SA Teukolsky, WT Vetterling and BP Flannery (1992) Numerical Recipes in Fortran 77: The Art of Scientific Computing, Cambridge University Press, New York.

Wolf AV, MG Brown and PG Prentiss (1984) In Crc Handbook of Chemistry and Physics(Eds, Weast, RC, MJ Astle and WH Beyer) CRC Press, Boca Raton, FL: pp. D-235.

79

Chapter 5: ScFv-Based Immunoadsorbent 5.1 INTRODUCTION

In Chapter 2, a model anti-β2m immunoadsorbent was created by immobilizing whole

BBM.1 antibodies onto porous agarose gel beads. While the molar binding activity of the

immobilized BBM.1 antibody was lower than expected (6%), its β2m-adsorption site density

(ρ′s = 0.030 ± 0.002 mg-β2m/mL-settled-gel) was sufficient to conduct preliminary in vitro

research with a VFPR prototype. The ideal immunoadsorbent for this application should

possess a high β2m-adsorption site density (ρ′s >1 mg-β2m/mL-settled-gel), so as to reduce

the hold-up and/or loss of valuable plasma proteins during extracorporeal therapy. Single-

chain variable region antibody fragments (scFv) should theoretically allow for higher

effective β2m-adsorption site densities because they are smaller in size than whole

antibodies. ScFvs are also genetically defined and amenable to microbial expression and in

vitro evolution. These potential advantages of scFvs over whole antibodies motivated the

creation of the BBM.1 scFv-based immunoadsorbent that is described by this chapter.

5.2 METHODS

5.2.1 Labeling of β2m

Recombinant human β2m was prepared as previously described [Ameer et al., 2001]

and biotinylated using the FluoReporter® Biotin-XX protein labeling kit (Molecular Probes,

Eugene, OR). A 20 mg/mL working stock of biotin-XX (sulfosuccinimidyl ester, sodium

salt) in DMSO (dimethylsulfoxide) was prepared and a 10-fold molar excess was added to

1.6 mg/mL β2m in PBS 7.4 (phosphate buffered saline, pH 7.4: 10 mM PO4, 138 mM NaCl,

2.7 mM KCl). The labeling reaction was performed at this pH to inhibit the reaction of the

sulfosuccinimidyl ester with the primary amines of lysine residues, thereby favoring the

labeling of the β2m at the N-terminus. The reaction mixture was incubated on a rocker for 90

min at room temperature and subsequently dialyzed overnight into PBS 7.4 at 4oC to remove

any unreacted biotin-XX using a 6-8 kD membrane (Spectrum Laboratories, Rancho

Dominguez, CA). The final concentration of β2m was determined using an extinction

coefficient of 20,065 M-1 cm-1 at 280 nm as previously described [Ameer et al., 2001], while

the degree of biotinylation (0.93 mol-biotin/mol-β2m) was determined following the kit

instructions.

80

Recombinant human β2m was labeled with Alexa Fluor® 488 (carboxylic acid,

succinimidyl ester), a fluorophore that is spectrally similar to fluorescein, but possesses

greater brightness and photostability (Molecular Probes). The protocol used was essentially

that described above for the biotinylation of β2m. However, 3-fold molar excess of a 5

mg/mL working stock of labeling agent was added to 1.1 mg/mL of β2m in PBS 7.4 for the

labeling reaction. The final concentration and degree of labeling (0.056 mole-

fluorophore/mole-β2m) was determined using the extinction coefficient previously described

[Ameer et al., 2001] and the protocol provided by Molecular Probes.

5.2.2 Cloning of VH and VL genes

The BBM.1 antibody-producing hybridoma cell line (HB-28) was purchased from

ATCC (Manassas, VA) and grown in T-flask static culture at 37oC in a 5% CO2 atmosphere.

The growth media consisted of 90% RPMI 1640 medium (ATCC), 10% FBS (fetal bovine

serum), 100 u/mL penicillin, and 0.1 mg/mL streptomycin. The total RNA from 3x107 cells

was isolated and RT-PCR was performed using the RNeasy® Midi and the OneStep RT-PCR

kits from Qiagen (Valencia, CA). Various combinations of the primers (0.5 µM each)

provided in the Mouse Ig-Primer Set (Novagen, Madison, WI) were used along with 1 µg of

RNA and 40 units of RNase inhibitor (Promega, Madison, WI) in 50 µL RT-PCR reaction

volumes. The thermocycler was run for 1 reverse-transcription cycle of 30 min at 50oC, 1

DNA polymerase-activation cycle of 15 min at 95oC, 35 amplification cycles of 45 sec at

94oC, 1 min at 60oC, 1 min at 72oC and 1 final extension cycle of 10 min at 72oC.

The PCR products were run on 1.2 or 2.0% agarose gels stained with ethidium

bromide. Those displaying bands characteristic of VH and VL genes (about 500 base pairs in

length) were purified using the QIAquick kit (Qiagen) and ligated into the pSTBlue-1

plasmid (Novagen). The ligation products were used to transform NovaBlue SinglesTM

competent cells (included in the pSTBlue-1 Perfectly Blunt Cloning kit from Novagen),

which were plated onto LB (Luria-Bertani medium) agar plates containing 50 mg/mL

ampicillin. After incubating the plates overnight at 37oC, single colonies were each grown in

5 mL of LB containing 100-150 mg/L ampicillin at 37oC overnight, and their plasmids were

purified using the QIAprep® Spin Miniprep kit (Qiagen). The DNA inserts of the plasmid

clones were sequenced and translated into peptide sequences so that they could be compared

81

to the partial peptide sequences obtained through the N-terminal degradation of protein A-

purified BBM.1 antibody.

Twenty-two cycles of N-terminal degradation were performed on a sample of whole

BBM.1 antibody. For each degradation cycle, the two predominant residues were assigned to

one of two peptide chains based on a match with the published sequence of the MOPC-21

myeloma κ light chain [Svasti and Milstein, 1972]. This was done because the BBM.1

hybridoma cell line (HB-28) was created by fusing an anti-β2m B-cell with the X63-Ag8

myeloma [Brodsky et al., 1979], a descendent of the MOPC-21 myeloma [Kohler and

Milstein, 1975]. Both the X63-Ag8 and MOPC-21 myeloma cell lines have been shown to

secrete the MOPC-21 κ light chain as well as an IgG1 heavy chain [Kohler and Milstein,

1975].

5.2.3 Display of scFv fragment by yeast

The VH and VL genes cloned from the BBM.1 hybridoma were initially expressed as

a scFv fragment in a yeast display system [Boder and Wittrup, 1997] (Figure 5.1). This

approach was selected because the β2m-binding affinity of the scFv could readily be

characterized in a quantitative fashion and, if deemed necessary, would be in a vector that is

amenable to in vitro evolution [Boder et al., 2000].

5.2.3.1 Insert Assembly

The scFv DNA insert was assembled in a VH-(Gly4Ser)4-VL configuration via the

splicing by overlap extension (SOE) method [Horton et al., 1989]. All of the PCR reactions

were performed using Cloned Pfu DNA polymerase and Cloned Pfu Reaction Buffer

(Stratagene, La Jolla, CA), following the manufacturer�s instructions except where otherwise

noted. During the first round of PCR, the VH and VL DNA inserts were amplified from the

pSTBlue-1 plasmids (30 ng plasmid DNA in each 50 µL reaction volume) using the custom

primers shown in Figure 5.2 (0.2 µM each). The thermocycler was run for 1 cycle of 45 sec

at 98oC, 28 cycles of 45 at 98oC, 90 sec at 72oC, and 1 cycle of 10 min at 72oC. The resulting

VH and VL PCR products were purified using the QIAquick® Kit and quantitated by

measuring their absorbance at 260 nm.

82

The second round of PCR was initiated without primers and was performed in a

single 50 µL reaction volume with 77 ng of each VH and VL PCR product and 400 µM of

each dNTP (deoxynucleotide triphosphate). The thermocycler was run for 5 cycles of 1 min

at 96oC, 1 min at 53oC, 2 min at 72oC, and 1 cycle of 10 min at 72oC. The 5�-VH and 3�-VL

primers were then added (0.5 µM each) and the thermocycler was run for 15 cycles of 1 min

at 96oC, 1 min at 53oC, 1 min at 72oC, and 1 cycle of 10 min at 72oC. The resulting scFv

DNA insert was purified and quantitated as above.

5.2.3.2 Plasmid Construction

The purified scFv SOE PCR product and the pCTCON yeast display plasmid [Graff,

2002] (a derivative of the pCT302 plasmid [Boder and Wittrup, 1997] with a BamHI site

added 5� to the c-myc sequence) were digested with BamHI and NheI restriction enzymes for

more than 2 hours at 37oC, according to the manufacturer�s instructions (New England

Biolabs, Beverly, MA). The restriction digest products were purified using the QIAquick®

Kit, combined in an equimolar ratio (500 ng plasmid, 4 µg insert), and ligated using T4 DNA

ligase (Stratagene) following the manufacturer�s instructions. After incubating the ligation

reaction mixture at room temperature for more than 2 hours, the reaction was heat

deactivated at 65oC for 10 min. The ligation products were used to transform XL1-Blue

Supercompetent E. coli (Stratagene), following the manufacturer�s protocol, and plated on

LB agar plates containing 50 mg/mL ampicillin. Single colonies were each grown in 5 mL

of LB containing 100 mg/L ampicillin at 37oC overnight and their plasmid clones were

purified using the QIAprep® Spin Miniprep Kit. A plasmid clone with the desired in-frame

scFv insert was identified through DNA sequencing and labeled pEAG1.

5.2.3.3 Yeast Transformation, Growth, and Induction

EBY100 strain yeast cells [Boder and Wittrup, 1997] were transformed with pEAG1

through electroporation, plated onto SD-CAA agar plates (7 g/L yeast nitrogen base, 5.4 g/L

NaH2PO4, 8.6 g/L Na2HPO4, 5.0 g/L casamino acids, 20 g/L dextrose, Trp and Ura deficient)

and incubated for 2.5 days at 30oC. Cells originating from a single colony were grown in 5

mL of SD-CAA media (7 g/L yeast nitrogen base, 2.7 g/L NaH2PO4, 5.0 g/L Na2HPO4, 5.0

g/L casamino acids, 20 g/L dextrose) at 30oC on an orbital shaker for about 16 hours (OD600

83

= 4.0). A volume of the yeast suspension containing 5x107 cells (OD600=1 represents 1x107

cells/mL [Boder and Wittrup, 2000]) was centrifuged, re-suspended in 5 mL of SG-CAA

induction media (same as SD-CAA, but substituting galactose for dextrose), and incubated at

22oC on an orbital shaker for approximately 20 hours.

5.2.3.4 Yeast Labeling

The labeling of the yeast cells for FACS analysis was performed in a fashion similar

to that previously described [VanAntwerp and Wittrup, 2000]. Each of a series of 1.5 mL

centrifuge tubes were loaded with 1x106 EBY100 cells (transformed with pEAG1 and

induced with galactose). The tubes were centrifuged and the yeast pellets were washed with

500 µL of PBS/BSA (PBS 7.4 with 0.1% bovine serum albumin added as a carrier). Murine

anti-HA tag antibody (12Ca5 MAb, Roche, Basel, Switzerland) and biotinylated recombinant

human β2m were used as primary labeling agents at concentrations of 2 µg/mL and 1x10-11�

1x10-6 M, respectively. The primary labeling of each tube was carried out in 1.0 mL of

PBS/BSA at room temperature on a rocker for 30 minutes. The cells were spun down and

washed as above with ice-chilled PBS/BSA. Secondary labeling was conducted in 100 µL of

PBS/BSA on ice for 15 minutes, using 40 µL/mL each of streptavidin-phycoerythrin

(PharMingen, San Diego, CA) and FITC-conjugated anti-mouse IgG (Sigma, St. Louis, MO).

The cells were centrifuged at 4oC and washed quickly with 500 µL of ice-chilled PBS/BSA.

The labeled cell pellets were stored on ice and protected from light until FACS analysis.

Four additional yeast pellets were labeled for FACS analysis, which served as

controls. The labeling was performed as described above, except that: (1) the primary labels

were omitted; (2) biotinylated recombinant human β2m and streptavidin-phycoerythrin were

omitted; (3) the murine anti-HA tag antibody and FITC-conjugated anti-mouse IgG were

omitted, (4) un-biotinylated recombinant human β2m was added in 100-fold molar excess to

competitively inhibit the biotinylated β2m.

5.2.3.5 FACS Analysis

The labeled yeast cell pellets were each resuspended in approximately 1.0 mL of

PBS/BSA and analyzed with an Epics® XL FACS (fluorescence activated cell sorter;

Beckman Coulter, Fullerton, CA) in a fashion similar to those previously described [Boder

84

and Wittrup, 2000; VanAntwerp and Wittrup, 2000]. Samples were gated by light scattering

and then by FITC signal in order to avoid consideration of particles other than un-clustered

scFv-displaying yeast cells. The mean phycoerythrin (PE) signal for more than 2x104 scFv-

displaying cells labeled with each β2m concentration was recorded. SPHEROTM Rainbow

Calibration Particles (3.0-3.4 µm, Spherotech, Libertyville, IL) with six different known

densities of surface-immobilized FITC were also analyzed (>1x103 counted at each density)

to allow for the correlation of the mean FITC signal per cell to the mean number of scFv

fragments displayed by each cell.

5.2.3.6 Mathematical Modeling

Assuming a monovalent antibody-antigen binding interaction, the antibody-antigen

equilibrium dissociation constant, KD, is defined by Equation 5.1

2

2

[ ] [ ][ * ]

eq eqD

eq

scFv mK

scFv mβ

β≡ [5.1]

Here [scFv]eq, [β2m]eq, and [scFv*β2m]eq are the equilibrium concentrations (mole per L of

cell suspension during primary labeling) of dissociated antibody fragment, dissociated

antigen (β2m), and scFv fragment-antigen complex, respectively.

Assuming that the binding of β2m by the scFv fragment is the only reaction

consuming the dissociated species, [scFv]eq and [β2m]eq can be expressed in terms of other

variables as described by Equations 5.2 and 5.3.

0 2 0 0 2[ ] [ ] [ * ] [ ] [ * ]eq eq eqscFv scFv scFv m P Y scFv mβ β= − = − [5.2]

2 2 0 2[ ] [ ] [ * ]eq eqm m scFv mβ β β= − [5.3]

Here [scFv]0, [β2m]0, and [Y]0 are the initial molar concentrations of dissociated antibody

fragment, β2m, and yeast cells during the primary labeling step and P0 is the mean number of

scFv fragments displayed per cell (mole-scFv/mole-yeast). The value of P0 was

independently determined from the mean FITC signal and the calibration curve obtained

from the FACS analysis of the SPHEROTM standards.

The mean PE signal of the scFv-displaying population, F, is assumed to be a linear

function of [scFv*β2m]eq as described by Equation 5.4, where C1 and C2 are empirical

constants.

85

1 2 2[ * ]eqF c scFv m cβ= + [5.4]

Equations 5.1-5.4 can be combined and rearranged to yield Equation 5.5, which was

used to regress the values of KD, c1, and c2 from each set of F vs. [β2m]0 data .

( ) ( )212 0 0 0 2 0 0 0 0 0 2 0 2[ ] [ ] [ ] [ ] 4 [ ] [ ]

2 D DcF K m P Y K m P Y P Y m cβ β β = + + − + + − +

[5.5]

5.2.4 Secretion of scFv fragment by yeast

A His6-tag and a cysteine residue were added to the C-terminus of the secreted

version of the BBM.1 scFv fragment to facilitate its purification and subsequent

immobilization. This location was chosen to minimize the interference of the purification tag

and the immobilization bond with the β2m-binding site. It was deemed necessary to remove

the Lys-Arg sequence near the C-terminus of the VL gene because it is known to be cleaved

by the Kex2 protease within the trans-Golgi network of Saccharomyces cerevisiae [Bevan et

al., 1998; Rockwell and Fuller, 1998].

5.2.4.1 Plasmid Construction

The Lys-Arg sequence in the VL was removed by changing the Arg residue to Asn.

This was achieved through PCR (50 µL reaction volume) with the 5�-VH and 3�-Lys-Asn

primers (Figure 5.2, 0.25 µM each) and the pEAG1 plasmid (1 µL). Cloned Pfu DNA

polymerase and Cloned Pfu Reaction Buffer were used to carry out the reaction, following

the manufacturer�s instructions. The thermocycler was run for 1 cycle of 1 min at 98oC, 28

cycles of 1 min at 98oC, 2 min at 72oC, and 1 cycle of 10 min at 72oC. The resulting scFv

PCR product was ligated into the pCT302 plasmid essentially as described for the

construction of the pEAG1 plasmid, except that a 2:1 molar ratio of scFv insert to plasmid

DNA was used during the ligation reaction. A plasmid clone with the desired scFv insert,

pEAG2, was obtained from the ligation reaction products in the same manner as pEAG1.

The Kex2 protease resistant form of the BBM.1 scFv insert was amplified from the

pEAG2 plasmid through PCR with the 5�-VH and 3�-His6-Cys primers (Figure 5.2). The

PCR was performed as described for the creation of pEAG2, except that the thermocycler

was run for 1 cycle of 1 min at 98oC, 28 cycles of 1 min at 98oC, 1 min at 55oC, 1 min at

72oC and 1 cycle of 10 min at 72oC. The resulting scFv insert was ligated into the secretion

86

plasmid pRS-GALTwt [Shusta et al., 1999] in frame with the synthetic pre pro signaling

sequence [Clements et al., 1991], under control of the GAL1,10 promoter. The ligation

protocol was essentially that described for the construction of the pEAG1 from pCTCON,

except that the BamHI restriction enzyme was replaced with XhoI (New England Biolabs)

and a 4:1 molar ratio of scFv insert to plasmid DNA was used. A secretion plasmid clone

with the desired scFv insert, pEAG3, was obtained from the ligation reaction products in the

same manner as pEAG1 and pEAG2.

5.2.4.2 Yeast Transformation, Growth, and Induction

YVH10 yeast, a protein disulfide isomerase overexpressing strain of Saccharomyces

cerevisiae [Robinson et al., 1994], were transformed with pEAG3 and pRS314 (to add Trp-

resistance to allow selection on Trp deficient media) [Sikorski and Hieter, 1989] using the

lithium acetate/single-stranded carrier DNA/polyethylene glycol method [Agatep et al.,

1998]. Cells were plated onto selective SD-SCAA plates (6.7 g/L yeast nitrogen base, 7.5

g/L NaH2PO4, 5.4 g/L Na2HPO4, 20 g/L dextrose, 15 g/L agar, 182 g/L sorbitol, and

synthetic casamino acids: 40 mg/L adenine sulfate, 140 mg/L His, 190 mg/L Arg, 108 mg/L

Met, 52 mg/L Tyr, 290 mg/L Ile, 440 mg/L Lys, 200 mg/L Phe, 1260 mg/L Glu, 400 mg/L

Asp, 380 mg/L Val, 220 mg/L Thr, 130 mg/L Gly, deficient in Leu, Trp, and Ura) and

incubated at 30oC for 3 days.

Expansion of the transformed YVH10 cells was initiated by inoculating 50 mL of

SD-SCAA liquid media (same as SC-SCAA plates, but with agar and sorbitol omitted) with

cells originating from a single colony. After incubating the starter culture on an orbital

shaker at 30oC overnight (OD600 = 3.6), 30 mL of the starter culture was used to inoculate 6 L

of SD-SCAA. Each liter of SD-SCAA was placed into a 2.5 L fully baffled Tunair flask

(Shelton Scientific, Shelton, CT) and incubated at 30oC for 1 day (OD600 = 6.8). The yeast

cells were then centrifuged and resuspended in 6 L of YPG induction media (10 g/L yeast

extract, 20 g/L peptone, 20 g/L galactose) with 100 units/mL penicillin and 0.1 g/L

streptomycin added to inhibit bacterial contamination. Each liter of YPG was placed in a 2

L, smooth-bottomed Erlenmeyer flask and incubated at room temperature (approximately

22oC) for about 3 days (OD600 = 17.4). The cell suspension was then centrifuged and the

87

supernatant was 0.2 µm filtered and concentrated to an approximate volume of 400 mL using

a 10 kD Prep/Scale-TFFTM regenerated cellulose membrane (Millipore, Bedford, MA).

5.2.4.3 Protein Purification

The His6-tagged scFv fragment was purified from the concentrated cell culture

supernatant via nickel affinity chromatography, for which PBS 8.0 (phosphate buffered

saline, pH 8.0: 50 mM phosphate, 300 mM sodium chloride) was used with varying

imidazole concentrations. To remove metal contaminants, 5 mM sodium

ethylenediaminetetraacetic acid (EDTA) was added to the concentrated culture supernatant,

which was placed in a 400 mL stirred ultrafiltration cell with a 10 kD YM10 regenerated

cellulose disk membrane (Millipore). The cell was subsequently flushed with 2.8 L of PBS

8.0 to facilitate buffer exchange. To minimize the binding of un-tagged protein, 10 mM

imidazole was added and the protein was bound to a 5 mL column of Ni-NTA agarose gel

beads (Qiagen). The resin was washed with 60 mL of 20 mM imidazole and eluted with 30

mL of 250 mM imidazole. The eluted protein was further purified by size-exclusion

chromatography using Superose® 12 prep grade resin (Amersham Biosciences, Uppsala,

Sweden) eluted with PBS 7.4. The desired fractions were pooled and the concentration of

scFv was measured by reading the absorbance at 280 nm, using a molar extinction coefficient

of 51,130 L/mol cm-1 and a molecular weight of 29,032 g/mole. These values were

calculated from the amino acid sequence and the formula reported by Pace and co-workers

[Pace et al., 1995].

5.2.5 Immunoadsorbent based on scFv fragment

5.2.5.1 Protein Immobilization

Immediately prior to immobilization, the purified scFv fragment was reduced with

Immobilized TCEP (Tris[2-carboxyethyl] phosphine hydrochloride]) Disulfide Reducing Gel

(Pierce, Rockford, IL). The reaction was performed for one hour at room temperature on a

rocker in 3.5 mL of PBS 7.2 (phosphate buffered saline, pH 7.2: 100 mM PO4, 150 mM

NaCl) containing 15 mM EDTA, 33% TCEP gel by volume, and 2.0 mg/mL scFv fragment.

During the same hour, lysine Sepharose® 4B (Amersham Biotech) was activated with

sulfosuccinimidyl 4-(N-maleimidomethyl)cyclohexane-1-carboxylate (Sulfo-SMCC, Pierce).

88

Sulfo-SMCC is a heterobifunctional cross-linking agent that reacts with sulfhydryl and

primary amine groups. This reaction was also performed for one hour at room temperature

on a rocker, but in 4.5 mL of 150 mM sodium bicarbonate buffer (pH 8.8) containing 1.8

mg/mL Sulfo-SMCC and 22% swollen lysine Sepharose® 4B gel by volume.

Following the one-hour incubation, the activated lysine gel was rinsed (several times,

totaling 30 volumes) and re-suspend with ice-cold PBS 7.2. Immediately thereafter, the

reduced scFv fragment was removed from the TCEP gel by centrifuging it in a Micro Bio-

Spin® (Bio-Rad, Hercules, CA) column. The TCEP gel was rinsed with 1.0 mL of PBS 7.2

to improve the recovery of the scFv fragment. The scFv fragment immobilization reaction

was performed for 24 hours on a rocker at 4oC in 4.0 mL PBS 7.2 containing 4.4 mg scFv

fragment and 0.45 mL Sulfo-SMCC activated gel (settled bed volume). The number free

thiol groups per scFv fragment molecule, before and after contact with the TCEP gel, was

measured using the Thiol and Sulfide Quantitation kit obtained from Molecular Probes. The

kit instructions were followed except that the degassing performed by argon bubbling instead

of using vacuum desiccator.

The following day, the soluble scFv fragment was removed from the gel by

centrifuging it in a Micro Bio-Spin column and the gel was rinsed 4 times with 2.0 mL of

PBS 7.2. The gel was re-suspended in 2.0 mL PBS 7.2, containing 1 mM L-cysteine as a

quenching agent, and incubated overnight at 4oC on a rocker. After quenching, the gel was

centrifuged, rinsed four times as before, and resuspended in PBS 7.4. Equal volumes of the

reduced scFv fragment, the quenching buffer, and the eight rinses were assayed for protein

by SDS-PAGE (sodium dodecyl sulfate-polyacrylamide gel electrophoresis). A control

matrix was prepared by immobilizing L-cysteine onto lysine Sepharose® 4B gel following

the above protocol, omitting the scFv-protein.

5.2.5.2 Characterization

Alexa Fluor® 488-labeled recombinant human β2m (β2m-AF488, see Section 5.2.1)

was used to determine the β2m-adsorption capacity of the agarose-immobilized scFv

antibody fragment and control matrix. A series of 0.5 mL centrifuge tubes were each loaded

with 100 µL of 10% gel suspension in FCS/PBS (75% fetal calf serum, 25% PBS 7.4 by

volume), a saturating quantity of β2m-AF488 (16, 12 or 10 µg; 0.96 mg/mL stock), and

89

sufficient FCS/PBS to bring the total volume to 0.400 mL. The tubes were equilibrated at

37oC for 1 hour on a rocker and then centrifuged. From each tube, three 100 µL volumes of

supernatant were loaded into individual wells of a 96-well plate, which was also loaded with

calibration standards (0, 10, 20, 30, 40, and 50 mg/L of β2m-AF488 in FCS/PBS). The plate

was read by a Mithras LB 940 plate reader (Berthold Technologies, Bad Wildbad, Germany),

using excitation and emission wavelengths of 485 and 535 nm, respectively. A linear

calibration curve was generated and was used to determine the β2m-AF488 concentrations of

the experimental samples. The β2m-adsorption capacity of the agarose-immobilized scFv

antibody fragment was calculated from this data, using Equation 5.6.

( )0total

s eqgel

V C CV

ρ′ = − [5.6]

Here ρ′s is the adsorption site density (mg β2m per mL of settled gel), Vtotal is the total volume

of each tube (mL), Vgel is the settled-volume of the gel (µL), C0 is the initial β2m

concentration (mg/L), and Ceq is the concentration of desorbed β2m at equilibrium (mg/L).

For regeneration, the labeled gel was recovered from the centrifuge tubes, placed in a

Micro Bio-Spin® column, and centrifuged. The immunoadsorptive media was regenerated

by rinsing it four times with 2.0 mL of stripping buffer (300 mM glycine, pH 2.8). The

regenerated media was rinsed four times with 2.0 mL of PBS 7.4, and then rinsed once and

resuspended with FCS/PBS to make a 10% suspension. The adsorption capacity of the

regenerated immunoadsorptive media was measured as above.

The affinity of the regenerated immunoadsorptive media for β2m was assessed by

following the protocol used to determine the adsorption capacity, except that each tube was

loaded with twice the amount of gel along with a sub-saturating quantity of β2m-AF488 (6

µg). The calibration standards also spanned a lower concentration range (0, 0.5, 1.0, 2.5, 5.0,

10, 15 mg/mL).

Leaching of the scFv fragment by the stripping buffer was assayed through Western

blotting. Diluting it with 13 mL of 100 mM sodium phosphate, 1 mM EDTA, pH 8.0,

neutralized each 2.0 mL volume of stripping buffer. Equal volume samples of the

neutralized stripping buffer and similarly diluted scFv from the immobilization reaction were

run on SDS-PAGE with 5% 2-mercaptoethanol added to the sample buffer as a reducing

agent. A PVDF (polyvinylidene difluoride) membrane was used for blotting, which was

90

labeled with Anti-His HRP conjugate (using the included Anti-His HRP conjugate blocking

buffer) following the manufacturer�s instructions (Qiagen). However, PBS 7.4 was used

instead of Tris buffered saline. Colorimetric detection was performed using the Opti-4CNTM

substrate kit (Bio-Rad), again following manufacturer�s instructions.

5.2.6 Statistical Analysis

Measured quantities are reported as the mean ± the standard error of the mean (SEM),

except for the scFv immobilization density and the mass ratio of adsorbed β2m to

immobilized antibody, for which the error estimates correspond to the accuracy of the gel

volume measurement. The significance of the difference between two means was tested by

ANOVA (analysis of variance) using a two-tailed p value of 0.05. Regressions were

performed by minimizing the summed square error (SSE).

5.3 RESULTS

5.3.1 Cloning of VH and VL genes

As resolved by agarose gel electrophoresis, one combination of the Ig-Prime kit

heavy chain primers (MuIgVH5�-D and MuIgVH3�-2) and three combinations of the light

chain primers (MuIgκVL5�-B, MuIgκVL5�-C, and MuIgκVL5�-E, each with MuIgκVL3�-1)

yielded RT-PCR products that were characteristic of VH and VL genes (approximately 400

base pairs in length). The DNA sequences of two of the VL RT-PCR products (MuIgκVL5�-

B and MuIgκVL5�-C) were found to match the aberrant light chain sequence listed in the Ig-

Prime kit instructions [Carroll et al., 1988] and were discarded. The sequences of the

remaining VH and VL genes (Figure 5.3) were translated and compared to the peptide

sequencing results of the protein A-purified BBM.1 antibody.

Three different peptide chains were detected by N-terminal degradation, where only

two were expected for a pure monoclonal. The signal for one of the peptide chains was too

weak to determine its sequence with a high level of confidence, while the two predominant

peptide chains were found in approximately equal proportions. The sequence of the MOPC-

21 κ light chain was used to infer the sequence of the second peptide chain in the BBM.1

antibody sample. This peptide sequence matched the cloned VH sequence, but did not match

that of the MOPC-21 heavy chain [Milstein et al., 1974]. Meanwhile, the sequence of the

91

cloned VL gene did not match the sequence of the MOPC-21 κ light chain. These findings

suggested that the cloned VH and VL genes belonged to the anti-β2m antibody secreted by the

BBM.1 hybridoma.

5.3.2 Display of scFv fragment by yeast

The ability of the cloned VH and VL genes to bind β2m was confirmed by expressing

them as a scFv fragment in a yeast display format. The addition of 100-fold molar excess un-

biotinylated β2m effectively inhibited the binding of the biotinylated β2m, while the average

number of scFv fragments displayed by the pEAG1-transformed yeast was 2.x104 ± 0.3x104

mole-scFv/mole-yeast (P0). The three FACS titration curves that were used to determine the

value of the scFv-β2m dissociation equilibrium constant are summarized by Figure 5.4 (KD =

0.7 ± 0.3 nM = 0.008 ± 0.004 mg-β2m /L). Based on these results, it was concluded that the

cloned VH and VL genes belong to the anti-β2m antibody produced by the BBM.1 cell line.

5.3.3 Secretion of scFv fragment by yeast

Figure 5.5 gives the sequence of the secreted scFv fragment, while Figure 5.6

demonstrates the purity of the scFv fragment after purification by nickel affinity

chromatography. One minor peak and two major peaks were eluted from the size-exclusion

column (as resolved by monitoring the absorbance of at 280 nm). The minor peak

corresponded to the exclusion-limit of the resin, while the two major peaks (approximately

the same size) corresponded to the molecular weights of the scFv fragment and its dimer.

The fractions from the two major peaks were pooled to improve the yield of scFv fragment

preparation and used to produce the immunoadsorptive media. The yield of purified scFv

fragment per unit volume of culture was 1.5 mg/L.

5.3.4 Immunoadsorbent based on scFv fragment

The TCEP reducing gel increased the molar ratio of free thiol groups to scFv

fragments from less than 0.1% to 50%. At the end of the immobilization reaction, 25% of

the total, or 50% of the reduced scFv fragment, had bound to the Sulfo-SMCC-activated gel.

This corresponds to an immobilization density of 2.4±0.2 mg-scFv/mL-settled-gel. No

leaching of the scFv fragment from the immunoadsorbent was detected in the PBS rinses

92

(SDS-PAGE), cysteine quenching buffer (SDS-PAGE), or in the neutralized stripping buffer

(Western blot).

Initial β2m Concentration, C0 [mg/L]

40 30 25 Mean Significance

Before Regeneration (N = 3) [mg-ββββ2m/mL-settled-gel] 0.33 ± 0.04� 0.41 ± 0.01 0.48 ± 0.05 0.40 ± 0.04 p > 0.2

After Regeneration (N = 5) [mg-ββββ2m/mL-settled-gel] 0.41 ± 0.02 0.44 ± 0.02 0.43 ± 0.01 0.43 ± 0.01 p > 0.6

Mean [mg-ββββ2m/mL-settled-gel] 0.41 ± 0.01

Significance p > 0.2

The observed β2m-adsorption site density (ρ′s) did not significantly depend on the

β2m-concentration under saturating conditions, nor did it significantly change after one round

of regeneration (Table 5.1). The average measured value of ρ′s was 0.41 ± 0.01 mg-β2m/mL-

settled-gel, which corresponds to a binding activity of 42% (molar ratio of adsorbed β2m to

immobilized scFv fragment) for the immobilized scFv fragment. Under sub-saturating

conditions (C0 = 15 mg/mL), the regenerated immunoadsorbent possessed sufficient affinity

to bring the concentration down to Ceq = 1.0 ± 0.1 mg/L (N = 5).

* Various initial concentrations (C0) of β2m-AF488 were equilibrated with 10 µL volumes of the immunoadsorptive media (Vgel) in 0.400 mL of FCS/PBS (Vtotal) at 37oC for 1 hour. The equilibrium concentration of desorbed β2m-AF488 (Ceq) was measured and used to calculate the β2m-adsorption site density (ρ′s) using Equation 5.6. These experiments were conducted on the immunoadsorptive media before and after regeneration with 0.3 M glycine, pH 2.8. � N = 2

Table 5.1 β2m-Adsorption Site Density of the Immunoadsorptive Media (ρ′′′′s).*

93

5.4 DISCUSSION

The removal of β2m from human blood plasma has previously been investigated with

immunoadsorbents consisting of whole anti-β2m antibodies immobilized onto porous beads

[Mogi et al., 1989; Nakano et al., 1991; Vallar et al., 1995; Shabunina et al., 2001]. These

small-scale affinity chromatography experiments have demonstrated that an

immunoadsorbent can remove β2m from human plasma with an affinity that has not been

achieved with hydrophobic interaction-based adsorbents [Furuyoshi et al., 1998; Davankov

et al., 2000]. Furthermore, these antibody-based adsorbents were found to be highly specific

for β2m, while the specificity of hydrophobic interaction-based adsorbents continues to be a

concern [Tsuchida et al., 1998; Reiter et al., 2002]. To date, perhaps the most promising

anti-β2m immunoadsorbent has been reported by Vallar and co-workers [Vallar et al., 1995],

which consisted of monoclonal antibodies immobilized onto Sepharose® CL-4B gel beads.

This adsorbent was highly regenerable and possessed a β2m-adsorption site density (0.9 mg-

β2m/mL-settled-gel) that is expected to be sufficient, but not optimal for actual clinical

application (i.e. 350 mL settled volume of adsorbent required to remove 315 mg of β2m).

While the results of these preliminary investigations are encouraging, the challenge of

removing β2m from whole blood in a single extracorporeal device has not been addressed

until recently (Chapter 2, [Ameer et al., 2001]). More specifically, low concentrations of

β2m (3.2 mg/L) were removed from whole human blood in vitro at a therapeutically relevant

flowrate (200 mL-blood/min) using a novel, plasmapheretic extracorporeal device (the

VFPR) and an immunoadsorbent based on whole BBM.1 antibodies. The concentration of

β2m that was cleared by the VFPR device was limited by a low β2m-adsorption site density

(ρ′s = 0.030 ± 0.002 mg-β2m/mL-settled-gel), which was caused by the low molar binding

activity of the immobilized BBM.1 antibody (only 6% of the immobilized antibody bound

β2m). Nevertheless, the immobilized whole antibodies (BBM.1) that retained binding

activity demonstrated a high affinity for β2m (KD = 0.1 ± 0.1 mg/L) as well as the ability to

be regenerated repeatedly (>10x) without a detectable loss of binding activity. At the time, it

was hypothesized that the low β2m-adsorption site density was either caused by the excessive

deactivation of the monoclonal antibody by the immobilization chemistry (cyanogen bromide

94

activation of agarose) and/or the expression of an additional, unwanted immunoglobulin

chain (impurity) by the hybridoma cell line.

Research into the origin of the BBM.1 antibody-producing hybridoma cell line (HB-

28) has revealed that it was created using the X63-Ag8 myeloma [Brodsky et al., 1979],

which has been shown to secrete the MOPC-21 κ light and IgG1 heavy chains [Milstein et al.,

1974; Kohler and Milstein, 1975]. In light of this fact, protein-A purified BBM.1 antibody

was partially sequenced through N-terminal degradation. The results suggest that the protein

sample primarily consisted of the MOPC-21 light chain and an IgG heavy chain other than

the MOPC-21 IgG1 chain (presumably the anti-β2m heavy chain), with a trace amount

(<10%) of a third peptide chain (presumably the anti-β2m light chain). The apparent absence

of MOPC-21 IgG1 in the protein sample can be explained by the fact that protein A is known

to bind to IgG2b with a higher affinity than IgG1 [Ladisch, 2001] and that the BBM.1

antibody has been classified as IgG2b [Brodsky et al., 1979].

The optimization of an immunoadsorbent for the extracorporeal removal of β2m will

require the maximization of the β2m-adsorption site density to minimize the required volume

of immunoadsorbent. The volume of immunoadsorbent contained within the extracorporeal

device is an important parameter for the optimization of biocompatibility, as it is proportional

to the amount of blood plasma retained during therapeutic operation. One strategy for

achieving higher β2m-adsorption site densities is to use scFv antibody fragments as

immunoadsorption ligands instead of significantly larger whole antibodies (1 mg of scFv

fragment can bind 0.4 mg of β2m, whereas 1 mg of whole antibody can only bind 0.16 mg of

β2m). Another advantage of scFv fragments over whole antibodies is their ability to be

expressed by microbial vectors. This makes scFv fragments amenable to in vitro evolution in

a convenient yeast display format and provides more options for process optimization,

potentially resulting in a significant reduction in production cost. ScFv fragments are also

genetically defined, which offers the opportunity to eliminate the expression of unwanted

peptide chains by the source hybridoma cell line.

Motivated by the potential advantages of scFv fragments, the desirable affinity and

regeneration capacity of BBM.1, and the apparent MOPC-21 κ light chain contamination, an

immunoadsorbent for the removal of β2m was created that is based on BBM.1 scFv

fragments. The BBM.1 scFv was first expressed in a yeast display format to facilitate the

95

characterization of its phenotype and to enable the engineering of its properties (i.e. stability

and/or regeneration capacity under various conditions) through in vitro evolution, if it is

desired in the future.

The binding affinity of the yeast-displayed scFv fragment for β2m was quantitated by

FACS analysis. The measured value of KD (0.7 ± 0.3 nM = 0.008 ± 0.004 mg/L) is in

agreement with that previously reported for the agarose-immobilized whole BBM.1 antibody

(0.1 ± 0.1 mg/L) (Chapter 4, [Grovender et al., 2002]). This result is noteworthy from an

antibody engineering perspective, because the conversion of a whole antibody to a wild-type

scFv fragment can result in a significant decrease in affinity [Maynard et al., 2002].

Furthermore, our reported value for KD is well below the β2m concentration range expected

in the blood plasma of healthy individuals (1.0-3.0 mg/L) [Floege and Ketteler, 2001].

Hence, the yeast-displayed wild-type BBM.1 scFv fragment possesses an affinity for

recombinant human β2m that is optimal for the clinical treatment of DRA through

extracorporeal immunoadsorption.

Given the encouraging binding affinity of the yeast-displayed antibody fragment, the

scFv gene* was expressed by a yeast secretion vector. The selected protein expression and

purification methods produced enough of the scFv fragment so that a small volume of a

model scFv immunoadsorbent could be produced for investigational purposes. The molar

binding activity (42%) and the β2m-adsorption site density (ρ′s = 0.41 ± 0.01 mg-β2m/mL-

settled-gel) of the scFv-based adsorbent are significantly greater than those measured for the

whole BBM.1 antibody-based adsorbent (molar binding activity of 6%, ρ′s = 0.030 ± 0.002

mg-β2m/mL-settled-gel). This improvement can be attributed to the elimination of the

production of the MOPC-21 light chain by the cloning procedure. Hence, this work

demonstrates how the creation of a wild-type scFv fragment from an existing hybridoma cell

line can be used to separate desired antibody genes from contaminating ones. Under

saturating conditions (Ceq >> KD), the mass ratio of adsorbed β2m to immobilized antibody

(0.17 ± 0.02 mg-β2m/mg-scFv) is roughly equivalent to the theoretical limit for 100% active,

bivalent whole IgG antibody (0.16 mg-β2m/mg-antibody) and 70% higher than that actually

achieved by Vallar and co-workers (0.1 mg-β2m/mg-antibody) [Vallar et al., 1995].

* A Kex2 protease-resistant version.

96

Shabunina and co-workers [Shabunina et al., 2001] have immobilized whole, polyclonal anti-

β2m antibodies onto Sepharose® CL-4B at densities that range from 2 to 16 mg/mL-settled-

gel. Over this range the mass ratio of adsorbed β2m to immobilized antibody remained

constant (0.04 mg-β2m/mg-antibody). If this immobilization density can be achieved for the

BBM.1 scFv while maintaining a molar binding activity of 42%, a new immunoadsorbent

with a β2m-adsorption site density of 2.7 mg-β2m/mL-settled-gel could theoretically be

produced. This would represent a 3-fold increase over the β2m-adsorption site density

reported by Vallar and co-workers [Vallar et al., 1995], which is the highest reliable value

reported in the literature.*

This is the first time that a scFv-based adsorbent for the extracorporeal removal of

β2m has been reported�. Under saturating conditions, this new type of immunoadsorbent

binds a mass ratio of adsorbed β2m to immobilized antibody that is above the theoretical

limit obtainable with whole antibodies. Future work will involve the optimization of the

scFv fragment expression, purification, and immobilization methods. A large volume (100-

200 mL) of this scFv-based immunoadsorbent will be produced and used within a VFPR

device to remove pathologic levels (20-70 mg/L [Gejyo et al., 1986; Koch, 1992]) of β2m

from human blood. We expect that the immobilization density of the scFv fragment can be

increased sufficiently such that, when combined with the high mass ratio of adsorbed β2m to

immobilized antibody, a β2m-adsorption site density can be achieved that is significantly

greater than the highest reported to date (ρ′s = 0.9 mg-β2m/mL-settled-gel [Vallar et al.,

1995]). This increase in the β2m-adsorption site density should translate into a proportionate

decrease in the volume of adsorbent needed for extracorporeal therapy and the blood plasma

retained, thereby improving the biocompatibility of the device.

* Mogi and co-workers [Mogi et al., 1989] have reported a β2m-adsorption site density of 4.3 mg/mL. However, this value is not reliable because their reported antibody immobilization density (18.8 mg-antibody/mL-gel) corresponds to a mass ratio of adsorbed β2m to immobilized antibody (0.23 mg-β2m/mg-antibody) that is well above the theoretical limit (0.16 mg-β2m/mg-antibody). � To the best knowledge of the author and Thesis Advisory Committee.

97

Figure 5.1 Schematic diagram of yeast display. (A) The gene encoding the scFv fragment of interest is cloned into the pCT302 plasmid (or derivative) in frame with the Aga2p mating protein, which is under control of the GAL1,10 promoter. The EBY100 strain of Saccharomyces cerevisiae possesses a single, integrated copy of the Aga1p gene which is also under control of the GAL1,10 promoter. Upon induction by galactose, EBY100 cells transformed with pCT302 co-express Aga1p and the Aga2p-scFv fusion. Aga1p is covalently bound to the cell wall and the Aga2p-scFv fusion. (B) Anti-HA tag antibody, anti-c-myc tag antibody, and labeled antigen can be used to characterize the expression and activity of the scFv using a fluorescence-activate cell sorter (FACS). Objects are not drawn to scale.

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVH

VL

Yeast Cell Membrane

Yeast Cell Wall

scFv

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVH

VL

Yeast Cell Membrane

Yeast Cell Wall

scFv

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVHVL

β2m

BiotinFITC

Avidin-PEAnti-HA MAb

Anti-mouse IgG

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVHVL

β2m

BiotinFITC


Anti-mouse IgG

A B

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVH

VL

Yeast Cell Membrane

Yeast Cell Wall

scFv

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVH

VL

Yeast Cell Membrane

Yeast Cell Wall

scFv

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVHVL

β2m

BiotinFITC


Anti-mouse IgG

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVHVL

β2m

BiotinFITC


Anti-mouse IgG

A B

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVHVL

β2m

BiotinFITC


Anti-mouse IgG

Aga1p

| |S S| |S S| |

Aga2p HA C-mycVHVL

β2m

BiotinFITC


Anti-mouse IgG

A B

98

5�-VH: /NheI G ATC GAT CGA GCT AGC GAG GTT CAG CTG CAG CAG TC I D R A S E V Q L Q Q |-> VH 3�-VH: CC TCA GTC ACC GTC TCC TCA GGT GGT GGT GGT TCT GGT GGT GGT GGT TCT GGC S V T V S S G G G G S G G G G S G VH <-|-> Linker GGC GGC GGC TCC G G G S 5�-VL: GGC GGC GGC GGC TCC GGA GGA GGA GGA TCG GAC ATT CAG ATG ACC CAG G G G G S G G G G S D I Q M T Q Linker <-|-> VL 3�-VL: /BamHI TTC GGA GGG GGG ACC AAG CTG GAA ATA AAA CGG GCT GGA TCC GAT CGA TCG ATC F G G G T K L E I K R A G S D R S I VL <-| 3�-Lys-Asn: /BamHI TTC GGA GGG GGG ACC AAG CTG GAA ATA AAA AAC GCT GAT GGA TCC GAT CGA TCG F G G G T K L E I K N A D G S D R S VL <-|Lys-Asn| ATC I 3�-His6-Cys: /XhoI CTT ATT TCT GAA GAG GAC TTG CAC CAC CAC CAC CAC CAC TGT TAG TGA CTC GAG L I S E E D L H H H H H H C STP STP L E C-myc-tag <-|-> His-tag <-|Cys| Stop | GAT CGA TCG D R S

Figure 5.2 Custom primers used for PCR. The assembly of the scFv insert by SOE was performed using 5�-VH, 3�-VH, 5�-VL and 3�-VL. The inserts for pEAG2 and pEAG3 were made using 5�-VH, 3�-Arg-Asn and 3�-His6-Cys. The 3�-VL-Arg-Asn also reintroduces the 110th amino acid in the BBM.1 VL gene, which was omitted from the 3�-VL primer. The sequences of the 3� primers listed are the reverse compliment of those actually used.

99

VH: GAG GTT CAG CTG CAG CAG TCT GGG GCA GAG CTT GTG AAG CCA GGG GCC TCA 51 E V Q L Q Q S G A E L V K P G A S 17 GTC AAG TTG TCC TGC ACA CCT TCT GGC TTC AAT GTT AAA GAC ACC TAT ATA 102 V K L S C T P S G F N V K D T Y I 34 CAC TGG GTG AAA CAG AGG CCT AAA CAG GGC CTG GAG TGG ATT GGA AGG ATT 153 H W V K Q R P K Q G L E W I G R I 51 GAT CCT TCG GAT GGT GAT ATT AAA TAT GAC CCG AAG TTC CAG GGC AAG GCC 204 D P S D G D I K Y D P K F Q G K A 68 ACT ATA ACA GCA GAC ACA TCC TCC AAC ACA GTC TCC CTG CAG CTC AGC AGC 255 T I T A D T S S N T V S L Q L S S 85 CTG ACA TCT GAG GAC ACC GCC GTC TAT TAC TGT GCT AGA TGG TTT GGT GAC 306 L T S E D T A V Y Y C A R W F G D 102 TAC GGG GCT ATG AAC TAC TGG GGT CAA GGA ACC TCA GTC ACC GTC TCC TCA 357 Y G A M N Y W G Q G T S V T V S S 119

VL: GAC ATT CAG ATG ACC CAG TCT CCT GCC TCC CAG TCT GCA TCT CTG GGA GAA 51 D I Q M T Q S P A S Q S A S L G E 17 AGT GTC ACC ATC ACA TGC CTG GCA AGT CAG ACC ATT GGT ACA TGG TTA GCT 102 S V T I T C L A S Q T I G T W L A 34 TGG TAT CAG CAG AAA CCA GGG AAA TCT CCT CAG CTC CTG ATT TAT GCG GCA 153 W Y Q Q K P G K S P Q L L I Y A A 51 ACC AGC TTG GCA GAT GGG GTC CCA TCA AGG TTC AGT GGT AGT GGA TCT GGC 204 T S L A D G V P S R F S G S G S G 68 ACA AAA TTT TCT CTC AAG ATC AGG ACC CTA CAG GCT GAA GAT TTT GTA AGT 255 T K F S L K I R T L Q A E D F V S 85 TAT TAC TGT CAA CAA CTT TAC AGT AAA CCG TAC ACG TTC GGA GGG GGG ACC 306 Y Y C Q Q L Y S K P Y T F G G G T 102 AAG CTG GAA ATA AAA CGG GCT GAT 330 K L E I K R A D 110

Figure 5.3 VH and VL Genes Cloned from the BBM.1 Hybridoma.

100

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06

Initial B2m Concentration, mole/L

Nor

mal

ized

Flu

ores

cent

Sig

nal

Mean Data (N=3)

Model (Equation 5.5)

10-11 10-10 10-9 10-8 10-7 10-6

Initial β2m Concentration, [β2m ]0, mole/L

Figure 5.4 Titration of BBM.1-scFv displaying yeast with fluorescent β2m. Aliquots of EBY100 cells transformed with pEAG1 and displaying wild-type BBM.1-scFv fragment were labeled with various concentrations of biotinylated β2m. Streptavidin-PE was used to label the adsorbed β2m. The mean PE signal of the scFv-displaying population of each yeast aliquot was measured by a fluorescence-activated cell sorter (FACS). Error bars represent standard error of the mean (SEM).

101

N-terminal Flanking Sequence: /NheI GAA GCT CGG CCG GCT AGC GAG GTT CAG CTG CAG CAG TCT GGG GCA GAG E A R P A S E V Q L Q Q S G A E Spacer <-| |-> VH C-terminal Flanking Sequence: /BamHI GAA ATA AAA AAC GCT GAT GGA TCC GAA CAA AAG CTT ATT TCT GAA GAG GAC TTG E I K N A D G S E Q K L I S E E D L |Lys-Asn| VL <-| |-> C-myc-tag <-| CAC CAC CAC CAC CAC CAC TGT H H H H H H C |-> His-tag <-|Cys|

Figure 5.5 The scFv fragment secreted by YVH10 yeast transformed with pEAG3. The full sequences of the VH and VL genes are given by Figure 5.3.

Figure 5.6 SDS-PAGE of the secreted BBM.1-scFv fragment after nickel affinity purification. The reduced sample was treated with 5% betamercaptoethanol and boiled for 5 minutes to dissociate the scFv dimer.

ReducedNon-Reduced

ScFv Dimer

ScFv Monomer

ReducedNon-Reduced

ScFv DimerScFv Dimer

ScFv MonomerScFv Monomer

102

5.5 REFERENCES Agatep R, RD Kirkpatrick, DL Parchaliuk, RA Woods and RD Gietz (1998) Technical Tips Online.


Bevan A, C Brenner and RS Fuller (1998) "Quantitative Assessment of Enzyme Specificity in Vivo: P-2 Recognition by Kex2 Protease Defined in a Genetic System." Proceedings of the National Academy of Sciences of the United States of America. 95: 10384-9.

Boder ET, KS Midelfort and KD Wittrup (2000) "Directed Evolution of Antibody Fragments with Monovalent Femtomolar Antigen-Binding Affinity." Proc Natl Acad Sci USA. 97: 10701-5.

Boder ET and KD Wittrup (1997) "Yeast Surface Display for Screening Combinatorial Polypeptide Libraries." Nat Biotechnol. 15: 553-7.


Brodsky FM, WF Bodmer and P Parham (1979) "Characterization of a Monoclonal Anti-Beta-2-Microglobulin Antibody and Its Use in the Genetic and Biochemical Analysis of Major Histocompatibility Antigens." Eur J Immunol. 9: 536-45.

Carroll WL, E Mendel and S Levy (1988) "Hybridoma Fusion Cell Lines Contain an Aberrant Kappa Transcript." Molecular Immunology. 25: 991-5.

Clements JM, GH Catlin, MJ Price and RM Edwards (1991) "Secretion of Human Epidermal Growth Factor from Saccharomyces Cerevisiae Using Synthetic Leader Sequences." Gene. 106: 267-71.




Gejyo F, S Odani, N Yamada, N Honma, H Saito, M Suzuki and e al. (1986) "Beta-2-Microglobulin: A New Form of Amyloid Protein Associated with Chronic Hemodialysis." Kidney Int. 30: 385.

Graff C (2002) Antibody Engineering for Tumor Immunotherapy. MIT, Chemical Engineering: Cambridge.


Horton RM, HD Hunt, SN Ho, JK Pullen and LR Pease (1989) "Engineering Hybrid Genes without the Use of Restriction Enzymes: Gene Splicing by Overlap Extension." Gene. 77: 61-8.

Koch KM (1992) "Dialysis-Related Amyloidosis." Kidney Int. 41: 1416.

Kohler G and C Milstein (1975) "Continuous Cultures of Fused Cells Secreting Antibody of Predefined Specificity." Nature. 256: 495-7.

103

Ladisch MR (2001) Bioseparations Engineering: Principles, Practice, Economics, Wiley-Interscience, Now York.

Maynard JA, CBM Maassen, SH Leppla, K Brasky, JL Patterson, BL Iverson and G Georgiou (2002) "Protection against Anthrax Toxin by Recombinant Antibody Fragments Correlates with Antigen Affinity." Nat Biotechnol. 20: 597-601.

Milstein C, K Adetugbo, NJ Cowan and DS Secher (1974) In Progress in Immunology Ii. Vol. 1 (Eds, Brent, L and J Holborow) North-Holland Publishing Company: pp. 157-68.

Mogi M, M Harada, T Adachi, K Kojima and T Nagatsu (1989) "Selective Removal of Beta-2-Microglobulin from Human Plasma by High-Performance Immunoaffinity Chromatography." J Chromatogr B Biomed Sci Appl. 496: 194-200.

Nakano H, H Gomi, T Shibasaki, F Ishimoto and O Sakai (1991) "An Experimental Study on Selective Elimination of Beta-2-Microglobulin Using Immunoadsorption Method in Patients with Chronic Renal Failure." Biomater Artif Cells Immobilization Biotechnol. 19: 61-9.

Pace CN, F Vajdos, L Fee, G Grimsley and T Gray (1995) "How to Measure and Predict the Molar Absorption Coefficient of a Protein." Protein Sci. 4: 2411-23.

Reiter K, V Bordoni, G Dall'Olio, MG Ricatti, M Soli, S Ruperti, G Soffiati, E Galloni, V D'Intini, R Bellomo and C Ronco (2002) "In Vito Removal of Therapeutic Drugs with a Novel Adsorbent System." Blood Purification. 20: 380-8.

Robinson AS, V Hines and KD Wittrup (1994) "Protein Disulfide-Isomerase Overexpression Increases Secretion of Foreign Proteins in Saccharomyces-Cerevisiae." Bio-Technology. 12: 381-4.

Rockwell NC and RS Fuller (1998) "Interplay between S-1 and S-4 Subsites in Kex2 Protease: Kex2 Exhibits Dual Specificity for the P-4 Side Chain." Biochemistry. 37: 3386-91.


Shusta EV, MC Kieke, E Parke, DM Kranz and KD Wittrup (1999) "Yeast Polypeptide Fusion Surface Display Levels Predict Thermal Stability and Soluble Secretion Efficiency." J Mol Biol. 292: 949-56.

Sikorski RS and P Hieter (1989) "A System of Shuttle Vectors and Yeast Host Strains Designed for Efficient Manipulation of DNA in Saccharomyces-Cerevisiae." Genetics. 122: 19-27.

Svasti J and C Milstein (1972) "The Complete Amino Acid Sequence of a Mouse Kappa Light Chain." Biochem J. 128: 427-44.



VanAntwerp JJ and KD Wittrup (2000) "Fine Affinity Discrimination by Yeast Surface Display and Flow Cytometry." Biotechnol Prog. 16: 31-7.

105

Chapter 6: Afterword 6.1 SUMMARY AND CONCLUSIONS

The body of work presented in this thesis supports the feasibility of using an

extracorporeal immunoadsorptive VFPR to specifically remove β2m from blood for the

prevention and/or treatment of DRA (dialysis-related amyloidosis). Furthermore, this blood

detoxification technology platform could potentially be used to treat other diseases that are

caused by circulating molecules that are otherwise difficult to remove (sepsis, liver failure,

autoimmune disease, drug overdoses, and genetic disorders). The biocompatibility and

efficacy of the proposed therapy was evaluated with a model immunoadsorbent consisting of

whole BBM.1 antibodies immobilized onto porous agarose gel beads (Chapter 2).

Concurrently, a dynamic immunoadsorption model was developed for the VFPR that was

based upon the independent characterization of the mass-transfer processes within the VFPR

and the thermodynamic behavior of the model immunoadsorbent (Chapter 4). The molar

binding activity of the immobilized BBM.1 antibody was lower than expected (6%), but its

β2m-adsorption site density (0.030 ± 0.002 mg-β2m/mL-settled-gel) was sufficient for

preliminary research. Hence, this model immunoadsorbent was used in a VFPR prototype to

remove β2m from donated bags of human blood in a closed-loop circuit at a clinically

relevant flowrate (200 mL/min blood circulation rate). Over a two-hour operating period, no

significant change was detected in the complete blood count and the total mass of soluble

blood protein. Meanwhile, the plasma free hemoglobin increased at a rate deemed

acceptable for hemodialysis [Ameer et al., 1999]. This preliminary safety data supports the

feasibility of using an immunoadsorptive VFPR for the extracorporeal removal of β2m.

The high-affinity of the proposed β2m removal system was demonstrated by the

ability of the immunoadsorptive VFPR to bring the concentration of native donor baseline

β2m (1.3 ± 0.1 mg/L) to a level that was below the detectable limit of the assay (0.1 mg/L).

The immunoadsorbent was successfully regenerated and used to remove controlled amounts

(3.2 ± 2 mg/L) of recombinant human β2m from the same donated bags of human blood. The

dynamics of β2m clearance from the blood bags was predicted by the mathematical

immunoadsorption model, without using adjustable parameters. The predicted and

experimentally observed time-scales of β2m removal from the blood were in agreement with

106

that calculated by dividing the total cell-free blood path (445 mL) by the hemofiltration rate

(50 mL-plasma/min). This finding led to the conclusion that the mass-transfer processes

within the active plasma compartment of the VFPR prototype were not rate-limiting.

Furthermore, the process controlling the rate of β2m removal from the blood was the

hemofiltration rate, which was on the order of the supply rate of β2m into the circulation

(approximately 70 mL/min [Floege et al., 1991]). Both of these mass-transfer processes are

expected to be rate-controlling should this specific device design be used for the

extracorporeal removal of β2m.

The ideal extracorporeal β2m removal technology would detoxify blood at a rate that

is much faster than the supply rate of β2m to the circulation. In light of this, a new VFPR

prototype with a 22% longer microporous membrane was constructed. The macroscopic

mixing patterns within this new prototype were characterized using the same experimental

and mathematical methods that were used in the development of the dynamic

immunoadsorption model (Chapter 3). The compartmental macroscopic mixing model was

able to describe the residence-time distribution data (r2 > 0.94) over the range of process

conditions considered. This suggests that the plasma flux across the microporous membrane

was not a function of position, which was an assumption of the model derivation. Therefore,

the new VFPR prototype is expected to allow for a proportionate increase in the rate of β2m

removal (hemofiltration rates of 70-85 mL-plasma/min).

In order to reduce the hold-up and/or loss of valuable plasma proteins during

extracorporeal therapy, the ideal immunoadsorbent for the removal of β2m should possess a

high β2m-adsorption site density (>1 mg-β2m/mL-settled-gel). ScFv antibody fragments

should theoretically allow for higher effective β2m-adsorption site densities because they are

smaller in size than whole antibodies. This theoretical basis motivated the creation of the

BBM.1 scFv fragment and a scFv-based immunoadsorbent for a feasibility study (Chapter 5).

The molar binding activity (42%) and the β2m-adsorption site density (ρ′s = 0.41 ± 0.01 mg-

β2m/mL-settled-gel) of the scFv-based adsorbent were dramatically improved from that of

the whole BBM.1 antibody-based adsorbent (described above). This improvement was

attributed to the elimination of the expression of a non-β2m-binding immunoglobulin chain

by the cloning procedure. Under saturating conditions, the mass ratio of adsorbed β2m to

107

immobilized antibody is roughly equivalent to the theoretical limit for 100% active, bivalent

whole IgG antibody and 70% higher than the highest value reported in the literature for

immobilized anti-β2m whole antibodies (0.1 mg-β2m/mg-antibody) [Vallar et al., 1995].

Whole anti-β2m antibodies have been immobilized onto agarose gel beads at densities

ranging from 2 to 16 mg/mL-settled-gel, without a detectable decrease in the mass ratio of

adsorbed β2m (under saturating conditions) to immobilized antibody [Shabunina et al.,

2001]. If this immobilization density can be achieved for the BBM.1 scFv fragment through

the optimization of the immobilization process while maintaining a molar binding activity of

42%, a new immunoadsorbent could be produced with a β2m-adsorption site density of 2.7

mg-β2m/mL-settled-gel. This would represent a 3-fold improvement over the highest β2m-

adsorption site density reported to date [Vallar et al., 1995]. The ability of this hypothetical

adsorbent to remove β2m from whole blood was predicted using the VFPR

immunoadsorption model (Chapter 4) and a set of input parameters (Table 6.1)

corresponding to the large VFPR prototype (Chapter 3). According to the model calculations

(Figure 6.1), this immunoadsorptive VFPR should be able to reduce a pathologically elevated

β2m concentration of 60 mg/L* to a level that is within normal the normal range of healthy

individuals (1.0-3.0 mg/L [Floege and Ketteler, 2001]) over the 5-hour period. This

corresponds to 313 mg of β2m removed from the blood reservoir or twice the amount

reported to be removed by the kidneys daily (150 mg [Vincent et al., 1980]).

Increasing the adsorption site density of the immunoadsorbent should theoretically

allow for a proportionate decrease in the volume of adsorbent required for extracorporeal

therapy, thereby enhancing biocompatibility. In existing direct hemoperfusion devices such

as the Lixelle® [Furuyoshi et al., 1998] and Betasorb® [Ronco et al., 2001] columns, the

rate of β2m removal is directly proportional to the volume of adsorbent contained within

them. This is due to the low surface area to volume ratio of the relatively large (>400 µm)

adsorbent particles that are required for biocompatibility with whole blood for this

application. Therefore, a decrease in the adsorbent volume of these direct hemoperfusion

columns would come at the expense of a proportionate decrease in the β2m removal rate.

* Plasma β2m concentrations of chronic hemodialysis patients typically range 20-70 mg/L [Gejyo et al., 1986; Koch, 1992].

108

This is not expected to be the case for the VFPR, in which the relatively small adsorbent

particles should allow for a 3-fold decrease in the volume of the adsorbent without a

significant decrease in efficacy.

Parameter Value Units Parameter Value Units

0tAPCC = 0 mg/L Qm 75§ mL/min

0,

tBC iC = 0 mg/L R 46�

0,

tBR iC = 60* mg/L VBC 52.4� mL

0tgelC = 0 mg/L VBC,i 8.0, 7.5, 7.1, 6.7, mL

0tPLCCC = 0 mg/L 6.3, 6.0, 5.6, 5.3�

De 1.1 x10-10 � m2/s VAPC 175� mL

HBR 0.31� - Vbed 120� mL

KD 0.008§ mg/L VBR 7.7** L

mk 10-3� m/s VPLCC 20 mL

NBC 8�� - ε 0.4� -

NBR 3� - Φ 0.87 -

QBR 200§ mL/min sρ′ 2.7�� mg/mL

* Plasma β2m concentrations of chronic hemodialysis patients typically range 20-70 mg/L [Gejyo et al., 1986; Koch, 1992]. � From Table 3.6. � From Table 4.1. § Value determined for yeast-displayed BBM.1 scFv in Chapter 5. ** This value was chosen so that the blood reservoir would contain 318 mg of β2m at a clinically expected β2m concentration. This blood volume is larger than that which would actually be found in an actual patient (~5 L). �� From Table 3.4. �� Value for the hypothetical BBM.1 scFv-based immunoadsorbent described in Section 6.1.

Table 6.1 Immunoadsorption model input parameters for the large VFPR prototype loaded with the hypothetical scFv-based adsorbent.

109

0

10

20

30

40

50

60

0 1 2 3 4 5

Time, hours

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Blood Reservoir

Plasma Line

Plas

ma

ββ ββ 2m

Con

cent

ratio

n,C PL

CC ,

mg/

L

Blo

od ββ ββ

2m C

once

ntra

tion,

C BR,N

BR, m

g/L

Figure 6.1 Immunoadsorption model-predicted clearance of ββββ2m from whole blood by the large VFPR prototype loaded with the hypothetical scFv-based adsorbent. Chapter 4 describes the mathematical model in detail, Table 6.1 provides a complete listing of the input parameters used, and Chapter 3 describes the large VFPR prototype.

110

6.2 RECOMMENDATIONS FOR FUTURE WORK

The next milestone for this research project should be the production of 0.1-1.0 L of a

new scFv-based adsorbent that possesses a β2m-adsorption site density greater than 2 mg-

β2m/mL-settled-gel. Based on the logic presented in Section 6.1, this is a reasonable goal

that will require the optimization of the production, purification, and immobilization methods

for the scFv fragment.

6.2.1 Optimization of ScFv Production

A greater than six-fold increase in the secretion level of recombinant glucose oxidase

by S. cerevisiae has been reported by changing from a shaker flask to a stirred tank batch

fermentor and optimizing the rates of agitation and aeration [Kapat et al., 1998]. Therefore,

the effect of varying several culture parameters (mixing pattern, temperature, media

composition, oxygen level) on the secretion level of BBM.1 scFv (g-scFv/L-culture) by

YVH10 S. cerevisiae should be studied in a stirred tank batch fermentor. Furthermore, in

vitro evolution of the BBM.1 scFv fragment could be performed to increase the expression

level of the BBM.1 scFv in a yeast display format, which often correlates with secretion

efficiency [Shusta et al., 1999; Boder and Wittrup, 2000]. The secretion level of the wild-

type BBM.1 scFv fragment without the His6-tag should be studied to determine its effect on

the secretion efficiency. This type of purification tag has inhibited the secretion of certain

scFv fragments by yeast in the Wittrup Laboratory at MIT.*

It is possible that expressing the BBM.1 scFv fragment as inclusion bodies or as

soluble active protein in bacteria could be more efficient than the optimized yeast secretion

system [Datar et al., 1993; Martineau et al., 1998]. Therefore, bacterial expression systems

for the scFv fragment should also be investigated. Moving to a bacterial vector would also

open up the possibility of expressing the scFv as an intein fusion protein, which would offer

more alternatives for purification and subsequent immobilization through an N-terminal

cysteine residue or a C-terminal thioester group [Xu and Evans, 2001].

* Personal communication with Katarina Midelfort.

111

6.2.2 Optimization of ScFv Purification

The purification of the His6-tagged scFv fragment by nickel affinity chromatography

proved to be effective (Chapter 5). However, the fact that this purification method is

patented would present a definite drawback if the immunoadsorbent were to be

commercialized. Other affinity chromatography ligands that could potentially replace nickel

include thiol groups and recombinant human β2m. Activated Thiol Sepharose® 4B is

commercially available from Amersham Biosciences and recombinant human β2m could be

immobilized onto Sepharose® CL-4B (following the protocol used to immobilize BBM.1 in

Section 2.2.2). Alternatively, recombinant human β2m could be biotinylated (Section 5.2.1)

and bound to Streptavidin Sepharose® HP (Amersham Biosciences).

Following the initial purification of the scFv fragment by one of the above affinity

chromatography methods, one or two additional rounds of chromatographic purification

should be performed on the scFv fragment before it is used to treat a patient or animal model.

It is suggested that ion exchange be used to concentrate the scFv fragment followed by size-

exclusion chromatography, which will re-dilute the purified product.

6.2.3 Optimization of ScFv Immobilization

It is possible that the state of aggregation of the BBM.1 scFv fragment affects its

amenability for active immobilization. Therefore, the thermodynamics and kinetics of

dimerization should be characterized under various buffer conditions (salt concentration,

scFv concentration, pH, reducing agent concentration). Size-exclusion chromatography

could be used to obtain fractions rich in either monomers or dimers and to subsequently

determine the effect of changes in buffer conditions on the state of aggregation [Pavlinkova

et al., 1999]. Furthermore, the effect of varying several parameters on the immobilization

density and molar binding activity for the maleimide-thiol immobilization reaction should be

studied, including:

1. The length and hydrophobicity of the spacer arm, either expressed as part of the scFv

peptide or included in the chemical cross-linking agent.

2. The reducing conditions of the scFv fragment immediately prior to immobilization.

Ideally, 100% of the C-terminal free cysteine residues of the scFv fragments should

112

be reduced without reducing the disulfide bridges within the immunoglobulin folds.

Reducing agents such as immobilized TCEP gel (Section 5.2.5.1), soluble TCEP,

DTT (dithiothreitol), reduced glutathione, cysteine, or β-mercaptoethanol could be

used in various amounts and buffers. Soluble TCEP is reported to have an advantage

over other types of soluble reducing reagents in that it does not interfere with

maleimide-thiol reactions [Haugland and Blalgat, 1998]. This reaction should also be

performed in an oxygen-free environment (degassed buffers in a nitrogen or argon-

filled glove box).

3. The time, temperature, pH, salt concentration, and reducing agent concentration of

the maleimide-thiol immobilization reaction.

4. The scFv concentration and contacting scheme during the immobilization reaction.

Performing the immobilization reaction at low scFv concentrations could minimize

spontaneous dimerization (if it is not desired). Meanwhile, a high scFv concentration

could increase the conversion of the immobilization reaction. Therefore, performing

the immobilization reaction in a plug-flow format with a low concentration of scFv

could potentially be optimal, as it could minimize dimerization and back-mixing.

113

6.3 REFERENCES Ameer GA, G Barabino, R Sasisekharan, W Harmon, CL Cooney and R Langer (1999) "Ex Vivo Evaluation of a Taylor-Couette Flow, Immobilized Heparinase I Device for Clinical Application." Proc Natl Acad Sci USA. 96: 2350-5.


Datar RV, T Cartwright and CG Rosen (1993) "Process Economics of Animal Cell and Bacterial Fermentaions: A Case Study Analysis of Tissue Plasminogen Activator." Bio-Technology. 11: 349-57.




Gejyo F, S Odani, N Yamada, N Honma, H Saito, M Suzuki and e al. (1986) "Beta-2-Microglobulin: A New Form of Amyloid Protein Associated with Chronic Hemodialysis." Kidney Int. 30: 385.

Haugland RP and MK Blalgat (1998) In Immunological Protocols. Vol. 80 (Ed, Pound, JD) Humana Press Inc., Totowa, NJ: pp. 189-90.

Kapat A, JK Jung, YH Park, SY Hong and HK Choi (1998) "Effects of Agitation and Aeration on the Production of Extracellular Glucose Oxidase from a Recombinant Saccharomyces Cerevisiae." Bioprocess Engineering. 18: 347-51.

Koch KM (1992) "Dialysis-Related Amyloidosis." Kidney Int. 41: 1416.

Martineau P, P Jones and G Winter (1998) "Expression of an Antibody Fragment at High Levels in the Bacterial Cytoplasm." Journal of Molecular Biology. 280: 117-27.

Pavlinkova G, GW Beresford, BJM Booth, SK Batra and D Colcher (1999) "Pharmacokinetics and Biodistribution of Engineered Single-Chain Antibody Constructs of Mab Cc49 in Colon Carcinoma Xenografts." Journal of Nuclear Medicine. 40: 1536-46.

Ronco C, A Brendolan, JF Winchester, E Golds, J Clemmer, HD Polaschegg, TE Muller, G La Greca and NW Levin (2001) "First Clinical Experience with an Adjunctive Hemoperfusion Device Designed Specifically to Remove Beta-2-Microglobulin in Hemodialysis." Blood Purification. 19: 260-89.


Shusta EV, MC Kieke, E Parke, DM Kranz and KD Wittrup (1999) "Yeast Polypeptide Fusion Surface Display Levels Predict Thermal Stability and Soluble Secretion Efficiency." J Mol Biol. 292: 949-56.


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Vincent C, N Pozet and JP Revillard (1980) "Plasma Beta-2 Microglobulin Turnover in Renal-Insufficiency." Acta Clinica Belgica. 35: 2-13.

Xu MQ and TC Evans (2001) "Intein-Mediated Ligation and Cyclization of Expressed Proteins." Methods. 24: 257-77.

115

Appendix: Immunoadsorption Model FORTRAN 77 Program PROGRAM CIRCUIT C KM: MASS-TRANSFER COEFFICIENT [m/sec] C NRSTEP: NUMBER OF RADIAL STEPS [-] C RADIUS: AVERAGE BEAD RADIUS [micron] C TTIME: TOTAL INTEGRATION TIME [minutes] C C0: INITIAL PATIENT B2M CONCENTRATION [mg/L] C DT: SCALED TIME STEP [-] C DE: EFFECTIVE DIFFUSIVITY [m^2/sec] C PA1: OLD SCALED PATIENT CONCENTRATION C PA2: NEW SCALED PATIENT CONCENTRATION C KPA: PATIENT RUNGE-KUTTA PARAMETER C BL0: INITIAL SCALED BLOOD CHAMBER CONCENTRATION C BL1: OLD SCALED BLOOD CHAMBER CONCENTRATION C BL2: NEW SCALED BLOOD CHAMBER CONCENTRATION C KBL: BLOOD CHAMBER RUNGE-KUTTA PARAMETER C MEM1: OLD SCALED AVERAGE MEMBRANE CONCENTRATION C MEM2: NEW SCALED AVERAGE MEMBRANE CONCENTRATION C KMEM: MEMBRANE RUNGE-KUTTA PARAMETER C PL0: INITIAL SCALED PLASMA CHAMBER CONCENTRATION C PL1: OLD SCALED PLASMA CHAMBER CONCENTRATION C PL2: NEW SCALED PLASMA CHAMBER CONCENTRATION C KPL: PLASMA CHAMBER RUNGE-KUTTA PARAMETER C BE1: OLD SCALED BEAD CONCENTRATION C BE2: NEW SCALED BEAD CONCENTRATION C KBE: BEAD RUNGE-KUTTA PARAMTER C CC1: OLD SCALED COLLECTION CHAMBER CONCENTRATION C CC2: NEW SCALED COLLECTION CHAMBER CONCENTRATION C KCC: COLLECTION CHAMBER RUNG-KUTTA PARAMETER C VFPR1: OLD SCALED VFPR EXIT CONCENTRATION C VFPR2: NEW SCALED VFPR EXIT CONCENTRATION C KVFPR: VFPR EXIT RUNGE-KUTTA PARAMETER C KD: ANTIBODY-B2M DISSOCIATION CONSTANT, BASED ON C ===>>> BULK CONCENTRATION/SETTLED VOLUME C ===>>>>> [mg-B2m/L-total fluid] C DS: DENSITY OF B2M BINDING SITES [mg-B2m/settled-L-gel] C PHI: PARTITION COEFFICIENT [pore conc./surface conc.] C EPS: GEL BED VOID FRACTION [EMPTY VOL/BED VOL] C SPHI: GEL BEAD PORE VOLUME FRACTION [L-pores/L-bead] C VPLASMA: TOTAL PLASMA CHAMBER VOLUME [ml] C VBEAD: WET GEL BEAD VOLUME [ml] C VBLOOD(): BLOOD CHAMBER VOLUMES (INCL. CELLS) [ml] C VPATIENT: CELL-FREE PATIENT VOLUME (INCL. CELLS) [ml] C VCC: VOLUME OF PLAMSA COLLECTION CHAMBER (ml) C Q: CELL-FREE CIRCUIT FLOWRATE [ml/min] C QM: PLASMA FLOWRATE THROUGH MEMBRANE [ml/min] C XB: PLASMA FLOW BYPASS FRACTION [-] C TPROC: PROCESS TIME SCALE [sec] C TPAT: PATIENT SPACE-TIME [sec] C TBLOOD(): PLASMA RESIDENCE TIME OF BLOOD COMPARTMENT TANKS [sec] C TPLAS: PLASMA CHAMBER SPACE-TIME [sec]

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C TBEEXT: BEAD EXTERNAL MASS-TRANSFER TIME SCALE [sec] C TBEINT: BEAD INTERNAL MASS-TRANSFER TIME SCALE [sec] C ERROR: RELATIVE ERROR IN MASS BALANCE C TOLER: MASS BALANCE ERROR TOLERANCE C INBEAD: TOTAL B2M IN AND ON THE BEADS [mg] C ADSORBED: TOTAL B2M ADSORBED AT THE END OF SIMULATION C MAXERROR: THE MAXIMUM AMOUNT OF ERROR IN THE MASS BALANCE C MAXERRJ: THE TIME STEP NUMBER AT WHICH MAXERROR OCCURS C NPA: NUMBER OF PATIENT "TANKS-IN-SERIES" C NBL: NUMBER OF BLOOD COMPARTMENT "TANKS-IN-SERIES" C NPL: NUMBER OF PLASMA COMPARTMENT "TANKS-IN-SERIES" C PAMASS: MASS OF B2M IN PATIENT AT TIME T [MG] C BLMASS: MASS OF B2M IN BLOOD CHAMBER AT TIME T [MG] C PLMASS: MASS OF B2M IN PLASMA CHAMBER AT TIME T [MG] C MASS0: INITIAL MASS OF B2M IN THE SYSTEM [MG] C HCT0: PATIENT HEMATOCRIT C HCT(): BLOOD COMPARTMENT TANK HEMATOCRITS C TOTALVOL: TOTAL CELL-FREE, POLYMER-FREE, VOLUME OF SYSTEM [L] INTEGER I, J, M, NTSTEP, COUNT, NWRITE, MAXERRJ, NPA, NBL, NPL, X NRSTEP REAL*8 RADIUS, C0, KM, DT, KD, DS, PHI, INBEAD, TOLER, ERROR, X MAXERROR, DR, VPLASMA, VBEAD, VPATIENT,Q, XB, TPROC, X TPAT, TPLAS, TCC, TBEEXT, BL0, PL0, PAMASS, BLMASS, X PLMASS, DE, TBEINT, EPS, SPHI, VBLTOTAL, CC1, CC2, X MEM1, MEM2, VFPR1, VFPR2, KVFPR, KMEM, KCC, HCT0, X QMUPTOI, MASS0, TOTALVOL REAL*8, ALLOCATABLE :: BE1(:,:), BE2(:,:), PA1(:), PA2(:), X BL1(:), BL2(:), PL1(:), PL2(:), VBLOOD(:), TBLOOD(:), X KPA(:), KBL(:), KPL(:),KBE(:,:),ADSORBED(:), X DESORBED(:), HCT(:) C READ INPUT FILE OPEN(UNIT = 5, FILE='INPUT.DAT', STATUS = 'OLD') READ(5,*) BL0, PL0 READ(5,*) NPA, NBL, NPL READ(5,*) RADIUS READ(5,*) NRSTEP READ(5,*) TTIME READ(5,*) NWRITE READ(5,*) C0 READ(5,*) KM READ(5,*) DE READ(5,*) KD READ(5,*) DS READ(5,*) PHI READ(5,*) SPHI READ(5,*) EPS READ(5,*) VPATIENT VPATIENT = VPATIENT*1000 C DIMENSION ARRAYS ACCORDINGLY ALLOCATE ( PA1(1:NPA), PA2(1:NPA), BL1(1:NBL), BL2(1:NBL),

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X PL1(1:NPL), PL2(1:NPL), BE1(1:NPL,0:NRSTEP), X BE2(1:NPL,0:NRSTEP), KPA(1:NPA), KBL(1:NBL), X KPL(1:NPL), KBE(1:NPL,0:NRSTEP), ADSORBED(1:NPL), X DESORBED(1:NPL), VBLOOD(1:NBL), HCT(1:NBL), X TBLOOD(1:NBL) ) READ(5,*) HCT0 READ(5,*) (VBLOOD(I), I=1,NBL) READ(5,*) VPLASMA READ(5,*) VBEAD READ(5,*) VCC READ(5,*) Q READ(5,*) QM READ(5,*) XB READ(5,*) TOLER CLOSE(5) C CALCULATE TOTAL BLOOD CHAMBER VOLUME VBLTOTAL = 0 DO 5 I= 1,NBL VBLTOTAL = VBLTOTAL + VBLOOD(I) 5 CONTINUE C CALCULATE TIME SCALES TPAT = VPATIENT/Q*60 TPLAS = (VPLASMA-(1-EPS)*VBEAD)/((1-XB)*QM)*60 QMUPTOI = 0 DO 7 I = 1, NBL QMUPTOI = QMUPTOI + QM/VBLTOTAL*VBLOOD(I) HCT(I) = Q*HCT0/(Q-QMUPTOI) TBLOOD(I) = 60 * (1-HCT(I))*VBLOOD(I) / X (QM/VBLTOTAL*VBLOOD(I)+(1-HCT(I))*(Q-QMUPTOI)) 7 CONTINUE TBEEXT = (RADIUS*1E-6)*(VPLASMA-(1-EPS)*VBEAD)/ X (3*(1-EPS)*VBEAD*KM*SPHI) TBEINT = (RADIUS*1E-6)**2/DE TCC = VCC/QM*60 C DEFINE THE PROCESS TIME-SCALE TPROC = (VPATIENT+VBLTOTAL*BL0)/(1-XB)/QM*60 C CALCULATE THE SCALED TIME STEP IF ((TBEINT/(2.2*REAL(NRSTEP)**2)).LT.(TBEEXT*0.05)) THEN DT = TBEINT/TPROC/(2.2*REAL(NRSTEP)**2) PRINT*, 'INTERNAL DIFFUSION LIMITED.' ELSE DT = TBEEXT/TPROC*0.05 PRINT*, 'EXTERNAL DIFFUSION LIMITED.' END IF C CALCULATE THE SCALED RADIAL STEP

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DR = 1/REAL(NRSTEP) C CALCULATE THE INITIAL MASS OF B2M IN SYSTEM MASS0 = C0/1000 * ( VPATIENT*(1-HCT0) + X PL0*(VPLASMA-VBEAD*(1-EPS)) ) TOTALVOL = (VPATIENT*(1-HCT0) + VPLASMA X - (1-SPHI)*(1-EPS)*VBEAD + VCC)/1000 DO 8 I = 1, NBL MASS0 = MASS0 + C0/1000 * BL0 * VBLOOD(I) * (1-HCT(I)) TOTALVOL = TOTALVOL + VBLOOD(I) * (1-HCT(I))/1000 8 CONTINUE C BEGIN WRITING THE PARAMETER OUTPUT FILE OPEN(UNIT = 7, FILE='PARAMETER.DAT', STATUS='UNKNOWN') WRITE(7,20) 'INITIAL BLOOD CHAMBER CONCENTRATION: ', BL0 WRITE(7,20) 'INITIAL PLASMA CHAMBER CONCENTRATION: ', PL0 WRITE(7,20) 'PARTICLE RADIUS: ', RADIUS, ' MICRONS' WRITE(7,25) 'NUMBER OR RADIAL STEPS: ', NRSTEP WRITE(7,20) 'TOTAL INTEGRATION TIME: ', TTIME, ' MINUTES' WRITE(7,20) 'INITIAL B2M CONCENTRATION: ', C0, ' MG/L' WRITE(7,20) 'SCALED TIME STEP: ', DT WRITE(7,20) 'TIME STEP: ', DT*TPROC, ' SECONDS' WRITE(7,20) 'MASS-TRANSFER COEFFICIENT: ', KM, ' M/SEC' WRITE(7,20) 'EFFECTIVE DIFFUSIVITY: ', DE, ' M^2/SEC' WRITE(7,20) 'BULK DISSOCIATION CONSTANT: ', KD, ' MG-B2M/L' WRITE(7,20) 'BINDING SITE DENSITY: ', DS, ' MG-B2M/SETTLED-L' WRITE(7,20) 'PARTITION COEFICIENT: ', PHI WRITE(7,20) 'PORE VOLUME FRACTION: ', SPHI, X ' PORE/BEAD VOLUME' WRITE(7,20) 'SETTLED-BED VOID FRACTION: ', EPS WRITE(7,20) 'PATIENT VOLUME (CELLS INLC.): ', X VPATIENT/1000, ' L' DO 10 I = 1, NBL WRITE(7,15) 'BLOOD CHAMBER TANK ',I, X ' VOLUME: ', VBLOOD(I), ' ML' 10 CONTINUE WRITE(7,20) 'TOTAL BLOOD CHAMBER VOLUME: ', VBLTOTAL, 'ML' WRITE(7,20) 'TOTAL PLASMA CHAMBER VOLUME: ', VPLASMA, ' ML' WRITE(7,20) 'TOTAL BEAD VOLUME: ', VBEAD, ' ML' WRITE(7,20) 'TOTAL INITIAL CELL-FREE VOLUME: ', TOTALVOL,' L' WRITE(7,20) 'INITIAL TOTAL B2M IN SYSTEM: ', MASS0, ' MG' WRITE(7,20) 'MASS ERROR TOLERANCE: ', TOLER WRITE(7,20) 'CIRCULATION FLOWRATE (CELL INCL.): ', X Q, ' ML/MIN' WRITE(7,20) 'PATIENT HEMATOCRIT: ', HCT0, ' HCT' DO 11 I = 1, NBL WRITE(7,15) 'BLOOD CHAMBER HCT,', I,': ', HCT(I), 'HCT' 11 CONTINUE WRITE(7,20) 'MEMBRANE PLASMA FLOWRATE: ', QM, ' ML/MIN' WRITE(7,20) 'PLASMA CHAMBER BYPASS FRACTION: ', XB WRITE(7,20) 'PATIENT SPACE-TIME: ', TPAT/60, ' MIN' DO 12 I = 1, NBL WRITE(7,15) 'BLOOD CHAMBER TAU,', I,': ', TBLOOD(I), 'SEC'

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12 CONTINUE WRITE(7,20) 'PLASMA CHAMBER SPACE-TIME: ', TPLAS, ' SEC' WRITE(7,20) 'INTERNAL BEAD TIME-SCALE: ', TBEINT, ' SEC' WRITE(7,20) 'EXTERNAL BEAD TIME-SCALE: ', TBEEXT, ' SEC' WRITE(7,20) 'PROCESS TIME-SCALE: ', TPROC/60, ' MIN' WRITE(7,25) 'NUMBER OF PATIENT TANKS: ', NPA WRITE(7,25) 'NUMBER OF BLOOD CHAMBER TANKS: ', NBL WRITE(7,25) 'NUMBER OF PLASMA CHAMBER TANKS: ', NPL 15 FORMAT(A19, I1,A10, E12.4, A20) 20 FORMAT(A30, E12.4, A20) 25 FORMAT(A30, I12, A20) C CONVERT KD AND DS FROM A BULK BASIS TO A PORE BASIS KD = KD * PHI DS = DS/SPHI/(1-EPS) C SPECIFY INITIAL CONDITIONS DO 30 I = 1, NPA PA1(I) = 1.0 30 CONTINUE DO 35 I = 1, NBL BL1(I) = BL0 35 CONTINUE DO 40 I = 1, NPL PL1(I) = PL0 DO 37 M = 0, NRSTEP BE1(I,M) = 0.0 37 CONTINUE 40 CONTINUE CC1 = 0 MEM1 = BL0 VFPR1 = 1/Q/(1-HCT0) * ( (1-XB)*QM*CC1 + XB*QM*MEM1 + X (Q-QM)*BL1(NBL)*(1-HCT(NBL)) ) C OPEN PROCESS OUTPUT FILE OPEN(UNIT=9, FILE='SYSTEM.OUT', STATUS = 'UNKNOWN') WRITE(9,'(8A14)') 'TIME, MIN','PATIENT','BLOOD', X 'PL CHAMB','LST BD CNTR','PL LINE','INBEAD, MG', X 'ERROR' WRITE(9,'(8E14.5)') 0.0, PA1(NPA), BL1(NBL), PL1(1), X BE1(NPL,NRSTEP),(XB*MEM1+(1-XB)*CC1), 0.0, 0.0 C INITIALIZE COUNTER AND MAXERROR COUNT = 0 MAXERROR = 0.0 MAXERRJ = 0 C CALCULATE THE NUMBER OF TIMESTEPS IN THE SIMULATION NTSTEP = INT(TTIME*60/TPROC/DT)+1 PRINT*, 'NUMBER OF TIMESTEPS CALCULATED' C PERFORM NUMERICAL INTEGRATION USING SECOND ORDER RUNGE-KUTTA

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DO 200 J = 1, NTSTEP C CALCULATE THE RUNGE-KUTTA PARAMETERS FOR THE PATIENT KPA(1) = PA1(1) + REAL(NPA)*0.5*DT*TPROC/TPAT*(VFPR1-PA1(1)) IF (NPA.GT.1) THEN DO 50 I = 2, NPA KPA(I) = PA1(I) + X REAL(NPA)*0.5*DT*TPROC/TPAT*(PA1(I-1)-PA1(I)) 50 CONTINUE END IF C CALCULATE THE RUNGE-KUTTA PARAMETERS FOR THE BLOOD CHAMBER KBL(1) = BL1(1) + X 0.5*DT*TPROC/TBLOOD(1)*(PA1(NPA)-BL1(1)) IF (NBL.GT.1) THEN DO 60 I = 2, NBL KBL(I) = BL1(I) + X 0.5*DT*TPROC/TBLOOD(I) * (BL1(I-1)-BL1(I)) C PRINT*, 'KBL(', I,') CALCULATED AS: ', KBL(I) 60 CONTINUE END IF C CALCULATE THE RUNGE-KUTTA PARAMETER FOR THE MEMBRANE KMEM = 0 DO 62 I = 1, NBL KMEM = KMEM + VBLOOD(I)*KBL(I)/VBLTOTAL C PRINT*, 'KMEM CALCULATED THROUGH TANK ', I, ' AS: ', KMEM 62 CONTINUE C CALCULATE THE RUNGE-KUTTA PARAMETERS FOR THE PLASMA CHAMBER KPL(1) = PL1(1) + X REAL(NPL)*0.5*DT*TPROC/TPLAS*(MEM1-PL1(1)) + X 0.5*DT*TPROC/TBEEXT*(BE1(1,0)/PHI-PL1(1)) IF (KPL(1).LT.0) THEN PRINT*, 'KPL(1) IS LESS THAN ZERO' PRINT*, 'TIME COUNTER (J) = ', J CLOSE (7) CLOSE (9) STOP END IF C SPECIFY BEAD SURFACE BOUNDARY CONDITION KBE(1,0) = (KM*PL1(1)+(DE/(DR*RADIUS*1E-6))*BE1(1,1)) / X (KM/PHI+DE/(DR*RADIUS*1E-6)) IF ((J.GT.10).AND.(KBE(1,0).EQ.0)) THEN

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PRINT*, 'ERROR: KBE(1,0) = ', KBE(1,0), ' J = ', J CLOSE(7) CLOSE(9) STOP END IF DO 65 M = 1, NRSTEP-1 KBE(1,M) = BE1(1,M) + 0.5*TPROC/TBEINT* X ((BE1(1,M+1)-2*BE1(1,M)+BE1(1,M-1))*DT/(DR)**2 X -DT*(BE1(1,M+1)-BE1(1,M-1))/(DR*(1-REAL(M)*DR))) X / (1+DS*KD/(KD+C0*BE1(1,M))**2) 65 CONTINUE C SPECIFY NO-FLUX AT THE CENTER KBE(1,NRSTEP) = BE1(1,NRSTEP) + TPROC/TBEINT * X (BE1(1,NRSTEP-1)-BE1(1,NRSTEP))*DT/(DR)**2 X / (1+DS*KD/(KD+C0*BE1(1,NRSTEP))**2) IF (NPL.GT.1) THEN DO 70 I = 2, NPL KPL(I) = PL1(I) + X REAL(NPL)*0.5*DT*TPROC/TPLAS*(PL1(I-1)-PL1(I)) + X 0.5*DT*TPROC/TBEEXT*(BE1(I,0)/PHI-PL1(I)) C SPECIFY BEAD SURFACE BOUNDARY CONDITION KBE(I,0) = (KM*PL1(I)+(DE/(DR*RADIUS*1E-6))*BE1(I,1)) / X (KM/PHI+DE/(DR*RADIUS*1E-6)) DO 67 M = 1, NRSTEP-1 KBE(I,M) = BE1(I,M) + 0.5*TPROC/TBEINT* X ((BE1(I,M+1)-2*BE1(I,M)+BE1(I,M-1))*DT/(DR)**2 X -DT*(BE1(I,M+1)-BE1(I,M-1)) / X (DR*(1-REAL(M)*DR))) / X (1+DS*KD/(KD+C0*BE1(I,M))**2) 67 CONTINUE C SPECIFY NO-FLUX AT THE CENTER KBE(I,NRSTEP) = BE1(I,NRSTEP) + TPROC/TBEINT * X (BE1(I,NRSTEP-1)-BE1(I,NRSTEP))*DT/(DR)**2 X / (1+DS*KD/(KD+C0*BE1(I,NRSTEP))**2) 70 CONTINUE END IF C CALCULATE THE RUNGA-KUTTA PARAMETER FOR THE COLLECTION CHAMBER AND VFPR KCC = CC1 + 0.5*DT*TPROC/TCC*(PL1(NPL)-CC1) KVFPR = ( (1-XB)*QM*KCC + XB*QM*KMEM + X (Q-QM)*KBL(NBL)*(1-HCT(NBL)) ) / Q/(1-HCT0) C CALCULATE THE PATIENT CONCENTRATIONS PA2(1) = PA1(1) + REAL(NPA)*DT*TPROC/TPAT*(KVFPR-KPA(1)) IF (NPA.GT.1) THEN DO 80 I = 2, NPA PA2(I) = PA1(I) + REAL(NPA)*DT*TPROC/TPAT*(KPA(I-1)-KPA(I)) 80 CONTINUE

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END IF C CALCULATE THE BLOOD COMPARTMENT CONCENTRATIONS BL2(1) = BL1(1) + DT*TPROC/TBLOOD(1) * (KPA(NPA)-KBL(1)) IF (NBL.GT.1) THEN DO 100 I = 2, NBL BL2(I) = BL1(I) + X DT*TPROC/TBLOOD(I) * (KBL(I-1)-KBL(I)) 100 CONTINUE END IF C CALCULATE THE NEW MEMBRANE CONCENTRATION MEM2 = 0 DO 102 I = 1, NBL MEM2 = MEM2 + VBLOOD(I)*BL2(I)/VBLTOTAL 102 CONTINUE C CALCULATE THE PLASMA CHAMBER AND BEAD CONCENTRATIONS PL2(1) = PL1(1) + REAL(NPL)*DT*TPROC/TPLAS*(KMEM-KPL(1))+ X DT*TPROC/TBEEXT*(KBE(1,0)/PHI-KPL(1)) IF (PL2(1).LT.0) THEN PRINT*, 'PL2(1) IS LESS THAN ZERO' PRINT*, 'TIME COUNTER (J) = ', J PRINT*, 'KMEM = ', KMEM PRINT*, 'KPL(1) = ', KPL(1) CLOSE (7) CLOSE (9) STOP END IF C SPECIFY BEAD SURFACE BOUNDARY CONDITION BE2(1,0) = (KM*KPL(1)+(DE/(DR*RADIUS*1E-6))*KBE(1,1)) / X (KM/PHI+DE/(DR*RADIUS*1E-6)) IF ((J.GT.10).AND.(BE2(1,0).EQ.0)) THEN PRINT*, 'ERROR: BE2(1,0) = ', BE2(1,0), ' J = ', J CLOSE(7) CLOSE(9) STOP END IF DO 105 M = 1, NRSTEP-1 BE2(1,M) = BE1(1,M) + TPROC/TBEINT* X ((KBE(1,M+1)-2*KBE(1,M)+KBE(1,M-1))*DT/(DR)**2 X -DT*(KBE(1,M+1)-KBE(1,M-1))/(DR*(1-REAL(M)*DR))) X / (1+DS*KD/(KD+C0*KBE(1,M))**2) 105 CONTINUE C SPECIFY NO-FLUX AT THE CENTER BE2(1,NRSTEP) = KBE(1,NRSTEP) + TPROC/TBEINT * 2 * X (KBE(1,NRSTEP-1)-KBE(1,NRSTEP))*DT/(DR)**2 X / (1+DS*KD/(KD+C0*KBE(1,NRSTEP))**2)

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IF (NPL.GT.1) THEN DO 110 I = 2, NPL PL2(I) = PL1(I) + X REAL(NPL)*DT*TPROC/TPLAS*(KPL(I-1)-KPL(I)) + X DT*TPROC/TBEEXT*(KBE(I,0)/PHI-KPL(I)) C SPECIFY BEAD SURFACE BOUNDARY CONDITION BE2(I,0) = (KM*KPL(I)+(DE/(DR*RADIUS*1E-6))*KBE(I,1))/ X (KM/PHI+DE/(DR*RADIUS*1E-6)) DO 107 M = 1, NRSTEP-1 BE2(I,M) = BE1(I,M) + TPROC/TBEINT* X ((KBE(I,M+1)-2*KBE(I,M)+KBE(I,M-1)) * X DT/(DR)**2-DT*(KBE(I,M+1)-KBE(I,M-1)) / X (DR*(1-REAL(M)*DR))) / X (1+DS*KD/(KD+C0*KBE(I,M))**2) 107 CONTINUE C SPECIFY NO-FLUX AT THE CENTER BE2(I,NRSTEP) = KBE(I,NRSTEP) + TPROC/TBEINT * X (KBE(I,NRSTEP-1)-KBE(I,NRSTEP))*DT/(DR)**2 X / (1+DS*KD/(KD+C0*KBE(I,NRSTEP))**2) 110 CONTINUE END IF C CALCULATE THE COLLECTION CHAMBER AND VFPR CONCENTRATIONS CC2 = CC1 + DT*TPROC/TCC*(KPL(NPL)-KCC) VFPR2 = ( (1-XB)*QM*CC2 + XB*QM*MEM2 + (Q-QM)*BL2(NBL)* X (1-HCT(NBL)) ) / Q / (1-HCT0) C RESET CONCENTRATION VARIABLES AND CALCULATE COMPARTMENT MASSES PAMASS = 0.0 BLMASS = 0.0 PLMASS = 0.0 INBEAD = 0.0 DO 120 I = 1, NPA PA1(I) = PA2(I) PAMASS = PAMASS + PA1(I)*VPATIENT*(1-HCT0)*C0/1000/REAL(NPA) 120 CONTINUE DO 130 I = 1, NBL BL1(I) = BL2(I) BLMASS = BLMASS + BL1(I)*VBLOOD(I)*(1-HCT(I))*C0/1000 130 CONTINUE DO 140 I = 1, NPL PL1(I) = PL2(I) PLMASS = PLMASS + X PL1(I)*(VPLASMA-(1-EPS)*VBEAD)*C0/1000/REAL(NPL) BE1(I,NRSTEP) = BE2(I,NRSTEP) ADSORBED(I) = 0.0

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DESORBED(I) = 0.0 DO 135 M = 0, NRSTEP-1 BE1(I,M) = BE2(I,M) ADSORBED(I) = 3*VBEAD*(1-EPS)/1000*DR*C0*(DS*(BE1(I,M) + X BE1(I,M+1))/2 X /(KD+C0*(BE1(I,M)+BE1(I,M+1))/2))/REAL(NPL) X * (1-(M+0.5)*DR)**2 * SPHI + ADSORBED(I) DESORBED(I) = 3*VBEAD*(1-EPS)/1000*DR*C0 * X (SPHI*(BE1(I,M)+BE1(I,M+1))/2) X / REAL(NPL) * (1-(M+0.5)*DR)**2 + DESORBED(I) 135 CONTINUE INBEAD = INBEAD + ADSORBED(I) + DESORBED(I) 140 CONTINUE MEM1 = MEM2 CC1 = CC2 VFPR1 = VFPR2 C CONFIRM THE B2M MASS BALANCE ERROR = 1 - ( PAMASS + BLMASS + PLMASS + INBEAD + X C0*VCC*CC1/1000 )/MASS0 IF ((ABS(ERROR)).GT.(ABS(MAXERROR))) THEN MAXERROR = ERROR MAXERRJ = J END IF C WRITE THE CONCENTRATION PROFILE TO THE OUTPUT FILES IF (INT((DBLE(NTSTEP)/DBLE(NWRITE))).EQ. X (INT(DBLE(J)-DBLE(COUNT) * X DBLE(NTSTEP)/DBLE(NWRITE)))) X THEN WRITE(9,'(8E14.5)') REAL(J)*DT*TPROC/60, X PA1(NPA), BL1(NBL), PL1(NPL), BE1(NPL,NRSTEP), X ((1-XB)*CC1+XB*MEM1), X INBEAD, ERROR 145 FORMAT(A35,E14.5) COUNT = COUNT + 1 END IF C WRITE MASS BALANCE ERROR MESSAGE AND QUIT IF (ABS(ERROR).GT.(TOLER)) THEN PRINT*, 'ERROR: B2M MASS BALANCE VIOLOATION.' WRITE(9, *) 'ERROR: B2M MASS BALANCE VIOLOATION.' WRITE(9, *) 'J = ', J, ' (NUMBER OF TIME STEPS)' WRITE(9, *) 'PERCENT ERROR: ', ERROR*100 CLOSE(7) CLOSE(9)

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STOP END IF 200 CONTINUE C FINISH WRITTING THE PARAMTER OUTPUT FILE WRITE(7,*) WRITE(7,20) 'TOTAL B2M IN THE BEADS: ', INBEAD, 'MG' WRITE(7,20) 'MAXIMUM MASS BALANCE ERROR: ',MAXERROR*100, X 'PERCENT' WRITE(7,25) 'TIME STEP NO. AT MAXERROR: ',MAXERRJ, ' ' WRITE(7,20) 'TIME AT MAX ERROR: ', X MAXERRJ*DT*TPROC/60, ' MIN' WRITE(7,20) 'FINAL TOTAL SYSTEM B2M: ', PAMASS + BLMASS + X PLMASS + INBEAD + C0*VCC*CC1/1000, ' MG' WRITE(7,20) 'FINAL MASS BALANCE ERROR: ', ERROR*100,'PERCENT' WRITE(7,20) 'FINAL MEAN PATIENT CONCENTRATION: ', X PAMASS/(1-HCT0)/VPATIENT*1000, 'MG/L' WRITE(7,20) 'FINAL MEAN PLASMA CHAMBER CONC.: ', X PLMASS/(1-EPS)/VPLASMA*1000,'MG/L' WRITE(7,20) 'FINAL PLASMA LINE CONC.: ', X (XB*MEM1+(1-XB)*CC1)*C0, 'MG/L' WRITE(7,20) 'FINAL BEAD CENTER CONC.S (MG/L): ' WRITE(7,300) (C0*BE1(I,NRSTEP), I=1,NPL) 300 FORMAT(10E14.5) C CLOSE OUTPUT FILES CLOSE(7) CLOSE(9) END

a fluidized immunoadsorption device for removing beta-2

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